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Optical fiber displacement sensor and its application to tuning fork response measurement
Precision Engineering 36 (2012) 620–628
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Precision Engineering journal homepage: www.elsevier.com/locate/precision
Optical fiber displacement sensor and its application to tuning fork response measurement Feilong Lin a,∗ , Stuart T. Smith a , Ghazanfar Hussain b a b
Center for Precision Metrology, UNC Charlotte, Charlotte, NC 28223, USA Photonics Division, National Institute of Lasers and Optronics, Islamabad 45650, Pakistan
a r t i c l e
i n f o
Article history: Received 28 February 2011 Received in revised form 16 May 2012 Accepted 24 May 2012 Available online 12 June 2012 Keywords: Knife edge sensor Displacement sensor Fiber optic beam conditioning Tuning fork
a b s t r a c t Optical sensors based on a knife edge obstruction represent an inexpensive method for stable, high signal to noise ratio (SNR), variable measurable range, low moving mass, compact size and high bandwidth displacement measurement. Two displacement sensor implementations have been evaluated in terms of noise and sensitivity as a function of the proximity of the knife edge relative to the source. Using a pigtailed laser diode and a photodiode as detector, the displacement of a knife blade across the output from the fiber varies the intensity of the laser transmitted to the photo detector. With this design, the range of the sensor is determined by the fiber diameter. This is compared to an inexpensive, LED optointerruptor and knife edge. The results show that laser diode and fiber illumination source sensor having an SNR of 40,000 at 1 kHz band width with working ranges as defined in this paper of between 4 and 90 m can be readily implemented. This is compared to a photo-interrupter based sensor for which the SNR is about 8000 with a displacement range of larger than 100 m. Based on these results, this sensing method is applied to the dynamic and static measurement of a tuning fork oscillator. © 2012 Elsevier Inc. All rights reserved.
1. Introduction Precision position sensing is a mature technology applied throughout precision machines and instrumentation. Today, the designer can select from a range of sensor methodologies that suits the particular application. For precision position measurement, the choice is typically between optical interferometry, optical lever, capacitance, inductance or transformer coupled methods and line scales based on optical, capacitive or inductive techniques. Light emitting diode (LED) and laser diode (LD) illumination sources are now produced at large scales on economical prices. Knife edge position sensors are more commonly used in the form of a focus detection configuration [1]. Typically, the light is reflected from a specular surface and focused in front of the detector [2–4]. The location of this focus along the optical path is dependent on the position of the specimen surface. Changes in position of the focus are, in turn, a function of the optical system that can be used to enhance positional sensitivity. Such designs are capable of producing displacement resolutions of better than one nanometer over ranges of a few micrometers with a bandwidth of 100 Hz [2]. The other configuration measures the intensity of the light as a direct function of the displacement of the knife edge across a focal spot,
∗ Corresponding author. Tel.: +1 704 687 8209; fax: +1 704 687 8255. E-mail addresses: fl[email protected], [email protected] (F. Lin). 0141-6359/$ – see front matter © 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.precisioneng.2012.05.004
hereafter referred to as a direct knife-edge method [4]. With this latter method and utilizing lock-in measurements of a modulated knife-edge, Puppin [4] has reported sub-nanometer resolution over a few micrometers with a relatively low bandwidth of less than 1 Hz. The light source beam is focused by a microscope objective down to a size of approximately 3 m full width at half maximum (FWHM). Here we present an investigation about the use of commercial LED and LD based sources for use with a direct knife edge and detector for displacement measurement. In a novel sensor implementation we used a fiber as the micrometer sized illumination source. For comparison, the second implementation uses the collimated beam from a photo-interrupter while using the same experimental set up. A major benefit of the knife edge is its relatively low mass. For designs in which the edge can be obtained from the mechanism itself this will add no mass to the moving component of the mechanism. Additionally, precisely manufactured knife edges will be insensitive to motions collinear with the edge thereby enabling two (and three in some implementations) axis sensing. The sensors outlined in this paper provide a working range of a few micrometers to millimeters (with different configurations) with SNR greater than 104 at MHz bandwidth. Originally designed as reference oscillators for clock timing, quartz tuning forks are often adapted for use as probe sensors for force and mass measurement [5,6] and are widely used as the sensing element in scanning probe microscopy [7] and other contact
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studies. When used as a sensor, its high Q (even in air) and selfsensing capability results in a compact sensing technique requiring the connection of only two wires to determine its response. This self-sensing feature eliminates the need for optical levers or other additional sensors commonly necessary with other contact probes. Feedback algorithms typically use combinations of the amplitude, frequency and phase of the fork vibration relative the excitation voltage. Directly or indirectly, current to the fork is used as a measure of the interaction between the fork and changes in its physical environment (gas, liquid or solid). We determine here the mechanical vibration amplitude by measuring the actual displacement of the tuning fork tines using the fiber-based sensor. 2. Principle of operation Both optical displacement sensors in this study are based on the measurement of the intensity of a light beam as a function of position of an obstruction e.g. knife edge placed in the optical path of the beam. Assuming the minimum detectable optical light intensity by the detector after amplification as Vmin and the maximum intensity as Vmax , the voltage range R = Vmax –Vmin , and the beam size (to be blocked, here it is about the diameter of the beam) D (m). The optical sensor noise Vsn (V) can be represented as Vn = GIn + Vsn
(1)
(V W−1 )
is the overall sensitivity or gain in the circuit, In where G (W) is the optical intensity noise and Vsn (V) is the intrinsic sensor noise. For random noise, this can be represented with a one side noise power spectral density S(f) (V2 Hz−1 ) as
ı2V =
f2
S(f )df
(2)
f1
If the power spectral density is assumed to be constant as So (V2 Hz−1 ), BW is the sensor bandwidth (Hz), the expected rms signal ıV (V) is
ı2V = ıV =
f2
So (f )df = So f f1
So f =
So ·
√
BW
(3) (4)
The output voltage from the photodiode and sensing circuit is the gain G multiplied by the incident optical power I plus the intrinsic measurement noise Vm (that includes noise of the sensor and signal conditioning circuitry), so we have V = GI + Vm
(5)
The sensor output voltage V can be calibrated as a displacement with sensitivity C (m V−1 ) C=
dx dV
(6)
Assuming the sensitivity is constant, a conservative estimated can be approximated from C>
D D D = = Vmax − Vmin GPs G(Imax − Imin )
(7)
The minimum detectable displacement can be approximated from dx D √ NEP √ So BW = D BW (8) · ıV ≈ ıx = GPs Ps dV where Ps is the maximum optical power at the detector (W), and NEP (W Hz−1/2 ) is the equivalent rms optical power incident on the detector and G (V W−1 ) is the sensitivity of the sensor and amplifier circuit. For a spectral density that is assumed constant over the
Fig. 1. Schematic diagrams indicating measuring principle of the knife edge sensor. (a) Photo-interrupter source and detector and (b) optical fiber displacement sensor.
bandwidth of measurement, the noise equivalent power NEP is estiSo /G. In theory, in addition to the unavoidable optical mated as and circuit noise, the NEP also depends on the photodiode noise which is the sum of thermal noise ij of the shunt resistance and the shot noise components id and iph resulting from the dark current (when operated in bias mode) and the photocurrent. For the photodiode of the experiments presented in this paper, the typical value of NEP is 1.5 × 10−14 W Hz−1/2 at 20 V bias (for 650 nm wavelength laser). The maximum optical power of diode source is 5 mW, and the smallest beam diameter D is typically about a few m (i.e. about 4 m in our application because of the small size of the optical fiber core). With√these values the resolution attainable (ıx) is in the range of 10−16 BW m Hz−1/2 . In practice, other noise sources So and the overall disas mentioned in Section 4, contaminate in the preliminary experiment described here placement resolution √ is around 10−11 BW m Hz−1/2 . Fig. 1(a) shows a configuration of a common photo-interrupter which is composed of an infrared emitter on one side and a shielded infrared detector on the other. Two small lenses are installed in front of them to collimate the beam from the source and collect the light at the detector. By emitting a beam of infrared light from one side to the other, the detector can generate a signal when an object passes through and blocks the beam. A normal knife edge is fixed in a moving object whose position is to be measured. When the edge moves up and down, it cuts through the beam and therefore, the detector produces a current that varies with the displacement of the motion of the knife edge. Since the beam is collimated, the location of the knife edge along the axis of the beam i.e. in the horizontal direction as drawn has little effect
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on the sensitivity. The sensing range is usually between 100 m and 500 m for commonly available commercial products. Based on the photo-interrupter, a more precise and flexible configuration is developed by using a laser coupled fiber as the emitter and a photodiode as the detector. In this configuration as shown in Fig. 1(b), the fiber becomes the illumination source and also conditions the laser beam. Laser diodes occupy volumes of only a fraction of a millimeter with the wire bonds being a substantial fraction of this volume. Additionally, given that fibers can be directly coupled to the diode known as butt coupling it is feasible to produce the illumination source and detector in a compact assembly while at the same time a short FWHM can be achieved from the fiber with a few micrometer diameter without any additional optics. There are a number of attributes with this design as follows: (i) the range of measurable displacement can be varied by changing the separation between the knife edge and the end of the fiber, (ii) when the edge is close to the fiber and the diameter of the fiber is a few micrometers, resolution of nanometer with bandwidths of kilohertz are readily obtained, (iii) the edge can be small, therefore it adds only a small mass to the object being measured, (iv) no electrical connection is necessary for the moving component (knife edge) of the sensor, (v) high bandwidth and fast response photodiodes are capable of hundreds of MHz bandwidth which is very useful for feedback control in high speed scanners, (vi) the whole setup is compact and low cost. The requirement for straightness of the knife edge and that it must remain at a fixed location along beam axis to maintain a constant sensitivity are limitations of this implementation.
3. Experimental measurement Experiments are set up to test the performances of both sensor implementations. Fig. 2(a) shows a block of diagram indicating the components used in the laser–photodiode experiment and is referred as Type A configuration (denoted as Type A). A laser diode driver (EK1101 from Thorlabs Inc.) energizes the diode which is, in turn, directly coupled with a fiber (FiberMax FMXL635-005). It is a single-mode fiber-pigtailed laser module provides a high fiber output power (5 mW at max.) while the fiber mode-field diameter is 4 m (FWHM is shorter than 4 m). High power light source requires low feedback resistors used in the photometric system to get the equal output compared with low power therefore reducing the time constant of the system. For the facility of setup, the end of the fiber is fixed onto a XY scanner (InsituTec IT-XY-100) having a range of 100 m in each axis. One end of a honed blade is glued on a manual micrometer stage to adjust the blade edge in x and y direction. A 3 mm PIN photodiode (FDS100 Thorlabs Inc.) operated in a biased mode (15 V) is used to measure the intensity of the laser. The photodiode was chosen for its small sensing area which reduces the noise, and it was operated in biased mode to have fast response times though the noise will be larger since the bias voltage generates a leakage current (dark current) resulting in shot noise [8]. A basic circuit with an LF411N operational amplifier was configured for transconductance with a selected feedback resistance value to provide a constant output voltage range corresponding the intensity of the LD i.e. inversely proportionate to LD power. Data acquisition system is built based on an NI LabVIEW Real-TimeTM system. Firstly turn on the laser, and tune the laser power to the required level. Adjust the feedback resistor in the circuit therefore the output of the amplifier will give an output close to 10 V to saturate the analog to digital converter (ADC). Record that value as Vfull , and then use micrometer stage to let the knife edge approach the fiber in x direction until the output reaches half of Vfull . After that, adjust the knife edge in y direction until it almost touch the fiber end, record the position as h. Finally position the XY scanner in x direction, record the position and the photodiode output and
Fig. 2. Block diagram of experimental configuration for the sensor tests. (a) Set up of LD and photodiode based knife edge sensor and (b) set up of photo-interrupter based knife edge sensor.
post-process the data. The h and power are varied for several tests in order afterwards and data are recorded respectively. Fig. 2(b) shows the similar setup for photo-interrupter experiment (denoted as Type B). The measurement circuit for the photo-interrupter contains AMP02 operational amplifier works as a differential amplifier to offset the output from the detector. An experimental evaluation of the output characteristics of both types of sensor has been undertaken. For the Type A it is necessary to measure the sensor output at different spacings between blade edge and the fiber. To avoid problems with backlash of our knife edge positioning system, in these experiments it was necessary to measure the distance from the detector, h varying from 0 mm to 3.1 mm, the latter value corresponding to the knife edge being as near to contact with the end of the fiber ferrule as was possible using the micrometer. Measurements of sensitivity and noise of this sensor were carried out at different settings of the laser power. Five levels of power at 1, 1.5, 2, 2.5 and 3 mW were tested. Sampling of the sensor output voltage was obtained at a rate of 100,000 samples per second and 1000 for measurements of noise and tracking of motion respectively. To measure the output from the sensors as a function of position of the knife edge relative to the sensor, a sinusoidal displacement x of 40 m amplitudes were used at a frequency of 0.1 Hz (Type A) and 1 Hz (Type B). For the Type B sensor, although the beam is, in principle, collimated, data at three locations along the y axis were recorded where h = 0 mm corresponded to the knife edge being centrally located between source and detector along the y axis.
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Table 2 Ranges and outputs defined by photo diode sensitivity when h varies.
Fig. 3. Stability tests of the measurement process for optical fiber displacement sensor.
h (mm)
Range (m)
Sensitivity peak (V m−1 )
90% sensitivity peak (V m−1 )
Output (V)*
1 1.5 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1
92.737 80.884 63.379 57.040 53.961 48.688 43.546 38.986 36.600 30.487 24.255 18.280 12.985 4.648
0.029 0.037 0.053 0.057 0.062 0.069 0.077 0.087 0.100 0.120 0.149 0.196 0.266 0.664
0.026 0.033 0.047 0.051 0.056 0.062 0.069 0.078 0.090 0.108 0.134 0.176 0.239 0.598
2.539 2.826 3.163 3.090 3.197 3.179 3.180 3.221 3.470 3.480 3.434 3.405 3.281 2.932
*
4. Results
Output is calculated based on the average sensitivity and range.
4.1. Stability Fig. 3 shows the output of Type A sensor data over a time period of 1 h during a time when the room temperature control was cycling approximately ±0.5 ◦ C. The experiment is set up as the knife edge sat approximately at the center of the fiber where it covered half the intensity (about 5 V at the output) corresponding to the photodiode reading half the maximum value. It contains a noise of about 10 mV PV value. The temperature of the lab recorded simultaneously shows a temperature drift which is negatively correlated to the drift of the sensor within the experimental setup. The drift is likely comes from photometric system or the thermal expansion of the devices in the metrology loop, i.e. photodiode mount or knife mount. Since the stability significantly limits the performance of the long-term measurement in changing temperature environment, a more stable environmental temperature control and better detector and circuit design with less thermal drift is required. 4.2. Dark current We vary the input laser power with corresponding gain setup and test the noise level as well the dark current noise. The results are demonstrated in Table 1. A higher illumination power level not only produces lower noise, but also enables a higher cut off frequency due to a lower gain in the photodiode circuit. The dark current noise also drops as the power goes up mainly because the feedback/load resistor is lower, and it weighs more in the total noise at the same time. 4.3. Sensor characteristic and calibration Fig. 4(a) shows the output of the photodiode (10,000 points raw data) and Fig. 4(b) shows the sensitivity (first fit the 10,000 raw data then use the derivative of the fitted equation) versus displacement of the knife edge in the x axis (see Fig. 2(a)) corresponding to different fibers to knife edge separation h at a laser power of 3 mW. From this figure the intensity looks Gaussian Table 1 Dark current noise with different power levels setup. Power (mW) Total noise Dark current (mV) 1 noise (mV) 1
Dark current/total (%)
1 1.5 2 2.5 3
8 12 20 24 26
2.356 1.477 0.906 0.693 0.655
0.193 0.172 0.182 0.167 0.172
along x axis which is the scanning direction with the sensitivity increasing as the blade approaches the fiber. It reaches to a maximum of 0.66 V m−1 where the blade almost touches the fiber (at h = 3.1 mm) and 0.02 V m−1 (at h = 0 mm) where the blade is closest to the detector. The core diameter of the fiber is 3–4 m. The reason for this trend is the Gaussian profile of the beam. Closest to the detector the beam is expanded and the detector is detecting the expanded portion of the beam. Whereas, when knife-edge is nearest to the fiber it intercepts almost the whole beam profile. Weibull function is chosen to fit the sensor displacement characteristic in Fig. 4(a). High order polynomials, Gaussian and other functions were fitted to these data sets but showed larger deviations. While the residual error for the Weibull function was lower for this function than others tried, there remained a systematic error of peak to valley amplitude of about ±6 mV. Combining a 6th order polynomial fit to these residuals it was possible reduce this to ±4 mV at h = 2.3 mm (see Fig. 4(c)). These two fitting equations only repeats when the y position (h) of the knife edge stays constant and the laser power does not change. Results of other laser power levels from 1 mW to 2.5 mW show similar characteristics. Fig. 4(b) is a plot of sensitivity with x for different separations h between the knife edge and fiber. It is reasonable to define the working range of the sensor at certain threshold values of sensitivity to provide an acceptable resolution. In this analysis, the range is defined by the translation in which the sensitivity remains within 10% of the peak sensitivity value. Table 2 shows the displacement ranges obtained at different values of h. Fig. 5(a) and (b) is respectively the output of the photointerrupter and its sensitivity versus displacement along x axis at different values of h (see Fig. 2(b)). The emitter is collimated by a lens molded into its mount. In principle, the sensitivity to motion of the blade in direction x are designed to be constant across the full 3.4 mm gap between emitter and detector of the interrupter (i.e. for different locations of h). In practice, the sensitivity reaches its maximum value at the center between the emitter and detector, while it drops when the blade is located on either side of this position. Nevertheless, the sensitivity reaches a maximum of 0.2 V m−1 . 4.4. Error sources
BW (cutoff) (Hz) 13,000 19,500 26,000 32,500 39,000
The noise sources come from the photodiode circuit, environmental temperature fluctuations and vibration, stability of the laser, blade edge roughness, and back-reflection from the surface of the blade disturbing the stability of the laser. Improper alignment of the fiber knife edge and detector will leads to coupling problems for multi-axis applications. It also
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Fig. 4. Performance of the Type A, laser diode based, displacement sensor. (a) The output of the photodiode versus displacement of the knife edge in the x axis corresponding to different fiber to knife edge separation h at a laser power of 3 mW, (b) the sensitivity of the photodiode versus displacement to different values of h at a laser power of 3 mW and (c) the fitting of the photodiode versus displacement characteristic and its residual error.
reduces the intensity coming to the detector therefore causing a decrease of the signal to noise ratio. The ambient light adds a certain amount noise to the detector. This can be avoided by covering the whole set up with an opaque
Fig. 5. Performance of the Type B, photo-interrupter based, displacement sensor. (a) The output of the photo-interrupter versus displacement of the knife edge in the x axis corresponding to different fiber to knife edge separation h and (b) the sensitivity of the photo-interrupter versus displacement to different values of h.
box, turning off the external light sources or using a band pass filter. In our test, we adapted the first two methods to limit the effect of ambient light. Temperature change will affect the knife edge’s length which mimics the sensor output. The thermal expansion coefficient of the steel (knife edge) is 11 × 10−6 C−1 , l = 0.005 m, with a temperature variations typically within 0.1 C, the systematic thermal error is about 5 nm. We prepared another block target using a silica slice with a straight line coated with aluminum. This will lower the thermal expansion to below 1 nm at the same conditions. Laser stability is another concern since there is light reflecting from the knife edge surface back into the fiber and subsequently to the laser diode. Although there is a feedback control for the diode current, this optical feedback may disturb the laser generation mechanism. By splitting a laser through an isolator and a fiber-coupler, and using one channel as a reference, the other as a measurement head, the isolator is able to attenuate the light coming back, and the instability of laser power can be solved by differential method. For calibration we used the XY positioner (InsituTec IT-XY-100) to calibrate the knife edge sensor. The linearity of the positioner is about 0.01% which corresponds to a 10 nm error at maximum position. Surface roughness of the edge will also cause deviations at the detector when the knife sensor is used in more than one axis. The photometric system noise is one main error source limiting the resolution. It is studied in the following section. 4.4.1. Configuration A The fundamental limits of the sensor system in displacement measurement come from the diode and diode driver, photo detector and photometric system and the sensitivity. In Section 4.2, the sensitivity is determined by the fiber core size (which provides a short FWHM) and the distance between the fiber core and the knife edge.
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Fig. 6. Laser diode driver supply current stability measurement.
The total noise current of the photometric system includes thermal noise ij of the shunt resistance (and channel resistance in the case of guard ring device) Rsh , the shot noise id and iph resulting from the dark current and the photocurrent, thermal noise current from the feedback resistor Rf , and amplifier noise current as expressed in Eq. (9) [8].
in
total
=
4kT 4kT 2 + 2q(id + iph ) + + iamp + (Vamp 2C)2 B Rsh Rf
(9)
where B is the noise bandwidth; k the Boltzmann’s constant, 1.38 × 10−23 (J K−1 ); T the temperature (K); q the 1.6 × 10−19 (C); id the shot current (A); iph the dark and photo current (A); iamp the amplifier input leakage current (A); Vamp the amplifier input noise voltage (V) and C is the amplifier input capacitance (F). For the photodiode used in the circuit, the NEP@650 nm is 1.5 × 10−14 W Hz−1/2 (35 MHz @20 V bias). The first two terms in Eq. (9) can be derived from NEP and the photo sensitivity [9] of the detector as 4.5 × 10−29 A2 Hz−1 . The feedback resistor Rf is about 2 k giving a value of around 10−29 A2 Hz−1 for the third term. The LF411N amplifier has 0.01 pA Hz−1/2 input noise current giving an estimated 10−28 A2 Hz−1 for the fourth term. The total current noise is 0.0124 pA Hz−1/2 which corresponds to approximately 1 V Hz−1/2 given the input impedance is around 108 . The LD driver circuit has a stability of less than 0.01% and output level of 0.1 A rms where the output current is up to 250 mA. A stability test with 3 mW laser power is shown in Fig. 6 from which an rms noise of 28 A which is at the limit of the measurement (9 A quantization noise from the 16 bits ADC) and corresponds to a stability of better than 0.02% of full scale at a bandwidth of 100 kHz. Noise data is collected when the distance h between the blade and fiber varies from near to the end of the fiber (h = 3.1 mm) to far from the fiber (h = 0 mm) while the power levels were maintained at a constant value ranging. Tests were carried out at different power levels ranging from 1 mW to 3 mW. Power spectrum measurements in Fig. 7(a) and (b) show similar distribution and magnitude over a measured bandwidth of 10 kHz for different values of h. The results show that the noise level does not change significantly with h, and the resolution was increased with reduced separation at the expense of shorter range. However, the noise spectrum values for a 3 mW source are about 1/9 to that measured with a 1 mW source. A 120 Hz and 240 Hz components are observed in the power spectrum which likely come from harmonic disturbance from the AC power lines (120 V at 60 Hz). To determine noise of the measurement system, similar measurements have been obtained with the translational stage maintained under closed loop control at a constant value of x = 50 m where the sensitivity of the sensor is at its peak. Fig. 8(a) is the power spectrum of noise when laser is controlled at different
Fig. 7. Noise level of the Type A sensor photodiode detector at different values of h. (a) Power spectrums of noise when the laser power is 1 mW and (b) power spectrums of noise when the laser power is 3 mW. Note that the range of the vertical scales (9 mV2 at 1 mW and 1 mV2 at 3 mW laser power) in proportion to the inverse square of the laser power.
power levels. It shows that the lower the power level, the higher of the noise level, a result again correlating with the inverse relationship between amplifier gain and laser power. It can be observed that the noise distribution exhibits a 1/f characteristic below about 1 kHz. Fig. 8(b) shows the cumulative power spectrum of noise as the laser power varies. Noise density is about 7.45 V Hz−1/2 at 1 mW laser power and 2.08 V Hz−1/2 at 3 mW which would correspond respectively to an rms noise of around 0.668 mV and 0.245 mV at a bandwidth of 1 kHz. With the sensitivity (at maximum point or x = 50 m) of 0.664 V m−1 at 3 mW power level and h = 3.1 mm, the displacement noise corresponds to around 0.37 nm, again at a bandwidth of 1 kHz. The SNR is about 40,000 for 3 mW and is 15,000 for 1 mW at 1 kHz bandwidth. Ignoring the 1/f at lower frequencies, the SNR will be higher. 4.4.2. Configuration B Photo-interrupter noise level data has been collected while the location of the blade along the optical axis (y axis) varies. As shown in Fig. 9, the power spectrum with the knife edge at different locations is little changed. A considerably larger 60 Hz AC power frequency and its odd harmonics appear in the spectrum (60 Hz, 180 Hz, and 300 Hz). This corresponds to about 60–70% of the total noise power. The noise density is about 74.1 V Hz−1/2 which would give an rms noise of around 7.4 mV corresponding to 37 nm with a sensitivity of 0.2 V m−1 at a bandwidth of 10 kHz and SNR of
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Fig. 8. Noise level of the photodiode when the laser power varies. (a) Power spectrums of noise with different laser powers and (b) cumulative power spectrums of noise with different laser powers.
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Fig. 10. Experimental setup for tuning fork characteristics measurement using optical fiber displacement sensor. Fig. 9. Power spectrums of the photo-interrupter noise at different values of h.
around 2700. In the absence of this 60 Hz spike, the cumulative power spectrum will drop down to around 9 mV2 and the rms noise will be in the region of 3 mV corresponding to an rms displacement noise of 14 nm and a corresponding SNR of better than 8000. The AC spike may come from unfiltered power used as a reference voltage and unshielded electrics. 4.5. Application: measuring tuning fork oscillation To evaluate the dynamic response, resolution, accuracy of the optical sensor, we applied this method to measure the dynamic as well as the amplitude of a tuning fork oscillator. Optical methods have been used to measure the absolute mechanical vibration amplitude and phase of the tuning fork for calibration and displacement sensitivity, i.e. a homodyne interferometer [10], and differential interferometry [11]. Ruiter et al. [12] measured the amplitude by gluing a fiber to one arm of the fork. Though being relatively easier to setup than an interferometric system, this method adds mass and stiffness to the fork that will, in turn, have a significant influence on its response. In this study, to demonstrate the high bandwidth and resolution of this optical fiber displacement sensor, the amplitude of tuning fork has been measured by using one arm of the fork as the knife edge to block light to the photo detector. The output (V) of the detector is calibrated to displacement using the nano-positioning XY scanner (InsituTec IT-XY-100) in a similar way in Section 4.3 where the knife edge is replaced by the tuning fork tine here. Fig. 10 shows the tuning fork attached to the XY scanner that is used to calibrate photodiode output voltage. Firstly the XY scanner is hold at a home position, and a sine wave voltage of amplitude 0.1 V is fed into the tuning fork directly using a signal generator (Tektronix AFG 3022B). The light intensity variation caused by the tine oscillation in y direction of the fork is measured by the photodiode. Then to calibrate the output of the photodiode, the stage of the XY scanner was translated in the y direction with an amplitude of 600 nm at a frequency of 1 Hz to block the light, where the fork tine is stationary. This calibration gives an rms value of 1.2 nm at 3.50 MHz bandwidth. Resolution is increased to 0.6 nm at 30 kHz and, assuming constant spectral density, 30 pm at 1 Hz bandwidth. For commercial displacement measurement interferometer or high resolution capacitance sensor, the resolution is about nanometer at couple kilohertz. This method provides a high resolution and bandwidth measurement with a limited range which is beneficial for specific applications where the dynamic displacement measurement is required.
By using the calibration information, Fig. 11(a) shows a time history of tuning fork oscillation at its resonant frequency of 32,752.36 Hz with a drive voltage of amplitude 0.1 V measured with a sampling rate of 300 ksps. A least square fitting yields an estimated amplitude of 265 nm. The standard deviation of the fitting error is 6.1 nm for about 5 periods data leading to an SNR of 31. Fig. 11(b) shows a time period data at the resonant frequency using self-sensing method from the piezoelectric signal. The of the fitting error is 0.027 V for about 4000 point data leading to an SNR of 24. The static amplitude has been measured by following two different methods. Fig. 12(a) shows the oscillation at 10 Hz with a drive voltage of amplitude 10 V (it was not possible to detect any measurable signal with a drive voltage of amplitude 0.1 V)with a sampling rate of 10 ksps and its fit. A 120 Hz oscillation of around 2 nm PV is observed to be superposed onto this 10 Hz signal that is interference from laboratory power lines. A least square fitting yields an estimated amplitude of 3.2 nm. The standard deviation of
Fig. 11. Tuning fork amplitude measurements comparison at resonant frequency. (a) Using the optical fiber displacement sensor and (b) using the self-sensing method from the piezoelectric signal.
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5. Conclusion This novel sensor based on the principle of photo-interrupter and knife edge does not require complex signal conditioning circuit while maintaining a high SNR at reasonable bandwidth. The relatively small number of components and the fact that all can be made using microelectronic processing technology makes it possible to produce a measurement system having a small footprint. Its low cost, low mass and compact size are desirable attributes for a nonintrusive, precision displacement sensor. Sensitivity goes up and the noise density remained relatively constant under the conditions of constant optical power level, reduced separation between the knife edge and source. In these measurements, it has been demonstrated that nanometer resolution in displacement measurement can be relatively easily obtained by placing knife edge close to the fiber having a core diameter of around 4 m. The tuning fork measurement demonstrates the optical sensor’s high dynamic response with MHz bandwidth at nanometer resolution. Further study is necessary to investigate how the quality of blade edge influences the performance. References
Fig. 12. Tuning fork amplitude measurements comparison at 10 Hz. (a) Using the optical fiber displacement sensor and (b) using the self-sensing method from the piezoelectric signal.
the fitting error is 1 nm for about 4 periods of data resulting in an SNR of 2 after removing the 120 Hz background noise. Fig. 12(b) shows time period data of tuning fork with the same driving signal using self-sensing method. The fitting signal’s amplitude is 0.005 V when the background noise is removed, and the standard deviation of the fitting error is 0.003 V for 5 periods data resulting in an SNR of 1. To validate this ‘static’ measurement, a stylus profiler (Rank Taylor Hobson Talystep) was also used as a second method to directly measure displacement of the tuning fork when driven at 10 V amplitude at 1 Hz for which an amplitude and standard deviation of 3.28 ± 0.2 nm was observed. The above two comparisons show that the optical knife-edge method’s SNR is twice that of the self-sensing method for amplitude measurement far from resonance. At or near the resonance of the tuning fork, the SNR of optical knife-edge methods is 30% higher than the self-sensing method.
[1] Fukatsu H, Kanagi K. Development of an optical stylus displacement sensor for surface profiling instruments. Microsystem Technologies 2005;11: 582–9. [2] Kohno T, Ozawa N, Miyamoto K, Musha T. High precision optical surface sensor. Applied Optics 1988;27:103–8. [3] Leach RK. Fundamental principles of engineering nanotechnology. Elsevier; 2010 [ISBN-13: 798-0-08-096454-6, Chapter 5]. [4] Puppin E. Displacement measurements with resolution in the 15 pm range. Review of Scientific Instruments 2005;76:105107. [5] Giessibl FJ. High-speed force sensor for force microscopy and profilometry utilizing a quartz tuning fork. Applied Physics Letters 1998;73:26. [6] Karrai K, Robert DG. Piezo-electric tuning fork tip – sample distance control for near field optical microscopes. Ultramicroscopy 1995;61: 197–205. [7] Edwards H, Taylor L, Duncan W, Melmed AJ. Fast, high-resolution atomic force microscopy using a quartz tuning fork as actuator and sensor. Journal of Applied Physics 1997;82:980. [8] Nick Bertone, Paul Webb. “Noise and Stability in PIN Detectors”, posted at www.ele.uva.es/∼pedro/optoele/photodiodes/noise.pdf. [9] HAMAMATSU. “Photodiode Technical Information”, posted at http://sales. hamamatsu.com/assets/applications/SSD/photodiode technical information. pdf. [10] Gucciardi PG, Bachelier G, Mlayah A, Allegrini M. Interferometric measurement of the tip oscillation amplitude in apertureless near-field optical microscopy. Review of Scientific Instruments 2005;76:036105. [11] Karrai K, Grober RD. Piezoelectric tip-sample distance control for near field optical microscopes. Applied Physics Letters 1995;66:1842. [12] Ruiter AGT, van der Werfag KO, Veermanag JA, Garcia-Parajoag MF, Rensenag WHJ, van Hulstag NF. Tuning fork shear-force feedback. Ultramicroscopy 1998;71:149–57.
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Precision Engineering journal homepage: www.elsevier.com/locate/precision
Optical fiber displacement sensor and its application to tuning fork response measurement Feilong Lin a,∗ , Stuart T. Smith a , Ghazanfar Hussain b a b
Center for Precision Metrology, UNC Charlotte, Charlotte, NC 28223, USA Photonics Division, National Institute of Lasers and Optronics, Islamabad 45650, Pakistan
a r t i c l e
i n f o
Article history: Received 28 February 2011 Received in revised form 16 May 2012 Accepted 24 May 2012 Available online 12 June 2012 Keywords: Knife edge sensor Displacement sensor Fiber optic beam conditioning Tuning fork
a b s t r a c t Optical sensors based on a knife edge obstruction represent an inexpensive method for stable, high signal to noise ratio (SNR), variable measurable range, low moving mass, compact size and high bandwidth displacement measurement. Two displacement sensor implementations have been evaluated in terms of noise and sensitivity as a function of the proximity of the knife edge relative to the source. Using a pigtailed laser diode and a photodiode as detector, the displacement of a knife blade across the output from the fiber varies the intensity of the laser transmitted to the photo detector. With this design, the range of the sensor is determined by the fiber diameter. This is compared to an inexpensive, LED optointerruptor and knife edge. The results show that laser diode and fiber illumination source sensor having an SNR of 40,000 at 1 kHz band width with working ranges as defined in this paper of between 4 and 90 m can be readily implemented. This is compared to a photo-interrupter based sensor for which the SNR is about 8000 with a displacement range of larger than 100 m. Based on these results, this sensing method is applied to the dynamic and static measurement of a tuning fork oscillator. © 2012 Elsevier Inc. All rights reserved.
1. Introduction Precision position sensing is a mature technology applied throughout precision machines and instrumentation. Today, the designer can select from a range of sensor methodologies that suits the particular application. For precision position measurement, the choice is typically between optical interferometry, optical lever, capacitance, inductance or transformer coupled methods and line scales based on optical, capacitive or inductive techniques. Light emitting diode (LED) and laser diode (LD) illumination sources are now produced at large scales on economical prices. Knife edge position sensors are more commonly used in the form of a focus detection configuration [1]. Typically, the light is reflected from a specular surface and focused in front of the detector [2–4]. The location of this focus along the optical path is dependent on the position of the specimen surface. Changes in position of the focus are, in turn, a function of the optical system that can be used to enhance positional sensitivity. Such designs are capable of producing displacement resolutions of better than one nanometer over ranges of a few micrometers with a bandwidth of 100 Hz [2]. The other configuration measures the intensity of the light as a direct function of the displacement of the knife edge across a focal spot,
∗ Corresponding author. Tel.: +1 704 687 8209; fax: +1 704 687 8255. E-mail addresses: fl[email protected], [email protected] (F. Lin). 0141-6359/$ – see front matter © 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.precisioneng.2012.05.004
hereafter referred to as a direct knife-edge method [4]. With this latter method and utilizing lock-in measurements of a modulated knife-edge, Puppin [4] has reported sub-nanometer resolution over a few micrometers with a relatively low bandwidth of less than 1 Hz. The light source beam is focused by a microscope objective down to a size of approximately 3 m full width at half maximum (FWHM). Here we present an investigation about the use of commercial LED and LD based sources for use with a direct knife edge and detector for displacement measurement. In a novel sensor implementation we used a fiber as the micrometer sized illumination source. For comparison, the second implementation uses the collimated beam from a photo-interrupter while using the same experimental set up. A major benefit of the knife edge is its relatively low mass. For designs in which the edge can be obtained from the mechanism itself this will add no mass to the moving component of the mechanism. Additionally, precisely manufactured knife edges will be insensitive to motions collinear with the edge thereby enabling two (and three in some implementations) axis sensing. The sensors outlined in this paper provide a working range of a few micrometers to millimeters (with different configurations) with SNR greater than 104 at MHz bandwidth. Originally designed as reference oscillators for clock timing, quartz tuning forks are often adapted for use as probe sensors for force and mass measurement [5,6] and are widely used as the sensing element in scanning probe microscopy [7] and other contact
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studies. When used as a sensor, its high Q (even in air) and selfsensing capability results in a compact sensing technique requiring the connection of only two wires to determine its response. This self-sensing feature eliminates the need for optical levers or other additional sensors commonly necessary with other contact probes. Feedback algorithms typically use combinations of the amplitude, frequency and phase of the fork vibration relative the excitation voltage. Directly or indirectly, current to the fork is used as a measure of the interaction between the fork and changes in its physical environment (gas, liquid or solid). We determine here the mechanical vibration amplitude by measuring the actual displacement of the tuning fork tines using the fiber-based sensor. 2. Principle of operation Both optical displacement sensors in this study are based on the measurement of the intensity of a light beam as a function of position of an obstruction e.g. knife edge placed in the optical path of the beam. Assuming the minimum detectable optical light intensity by the detector after amplification as Vmin and the maximum intensity as Vmax , the voltage range R = Vmax –Vmin , and the beam size (to be blocked, here it is about the diameter of the beam) D (m). The optical sensor noise Vsn (V) can be represented as Vn = GIn + Vsn
(1)
(V W−1 )
is the overall sensitivity or gain in the circuit, In where G (W) is the optical intensity noise and Vsn (V) is the intrinsic sensor noise. For random noise, this can be represented with a one side noise power spectral density S(f) (V2 Hz−1 ) as
ı2V =
f2
S(f )df
(2)
f1
If the power spectral density is assumed to be constant as So (V2 Hz−1 ), BW is the sensor bandwidth (Hz), the expected rms signal ıV (V) is
ı2V = ıV =
f2
So (f )df = So f f1
So f =
So ·
√
BW
(3) (4)
The output voltage from the photodiode and sensing circuit is the gain G multiplied by the incident optical power I plus the intrinsic measurement noise Vm (that includes noise of the sensor and signal conditioning circuitry), so we have V = GI + Vm
(5)
The sensor output voltage V can be calibrated as a displacement with sensitivity C (m V−1 ) C=
dx dV
(6)
Assuming the sensitivity is constant, a conservative estimated can be approximated from C>
D D D = = Vmax − Vmin GPs G(Imax − Imin )
(7)
The minimum detectable displacement can be approximated from dx D √ NEP √ So BW = D BW (8) · ıV ≈ ıx = GPs Ps dV where Ps is the maximum optical power at the detector (W), and NEP (W Hz−1/2 ) is the equivalent rms optical power incident on the detector and G (V W−1 ) is the sensitivity of the sensor and amplifier circuit. For a spectral density that is assumed constant over the
Fig. 1. Schematic diagrams indicating measuring principle of the knife edge sensor. (a) Photo-interrupter source and detector and (b) optical fiber displacement sensor.
bandwidth of measurement, the noise equivalent power NEP is estiSo /G. In theory, in addition to the unavoidable optical mated as and circuit noise, the NEP also depends on the photodiode noise which is the sum of thermal noise ij of the shunt resistance and the shot noise components id and iph resulting from the dark current (when operated in bias mode) and the photocurrent. For the photodiode of the experiments presented in this paper, the typical value of NEP is 1.5 × 10−14 W Hz−1/2 at 20 V bias (for 650 nm wavelength laser). The maximum optical power of diode source is 5 mW, and the smallest beam diameter D is typically about a few m (i.e. about 4 m in our application because of the small size of the optical fiber core). With√these values the resolution attainable (ıx) is in the range of 10−16 BW m Hz−1/2 . In practice, other noise sources So and the overall disas mentioned in Section 4, contaminate in the preliminary experiment described here placement resolution √ is around 10−11 BW m Hz−1/2 . Fig. 1(a) shows a configuration of a common photo-interrupter which is composed of an infrared emitter on one side and a shielded infrared detector on the other. Two small lenses are installed in front of them to collimate the beam from the source and collect the light at the detector. By emitting a beam of infrared light from one side to the other, the detector can generate a signal when an object passes through and blocks the beam. A normal knife edge is fixed in a moving object whose position is to be measured. When the edge moves up and down, it cuts through the beam and therefore, the detector produces a current that varies with the displacement of the motion of the knife edge. Since the beam is collimated, the location of the knife edge along the axis of the beam i.e. in the horizontal direction as drawn has little effect
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on the sensitivity. The sensing range is usually between 100 m and 500 m for commonly available commercial products. Based on the photo-interrupter, a more precise and flexible configuration is developed by using a laser coupled fiber as the emitter and a photodiode as the detector. In this configuration as shown in Fig. 1(b), the fiber becomes the illumination source and also conditions the laser beam. Laser diodes occupy volumes of only a fraction of a millimeter with the wire bonds being a substantial fraction of this volume. Additionally, given that fibers can be directly coupled to the diode known as butt coupling it is feasible to produce the illumination source and detector in a compact assembly while at the same time a short FWHM can be achieved from the fiber with a few micrometer diameter without any additional optics. There are a number of attributes with this design as follows: (i) the range of measurable displacement can be varied by changing the separation between the knife edge and the end of the fiber, (ii) when the edge is close to the fiber and the diameter of the fiber is a few micrometers, resolution of nanometer with bandwidths of kilohertz are readily obtained, (iii) the edge can be small, therefore it adds only a small mass to the object being measured, (iv) no electrical connection is necessary for the moving component (knife edge) of the sensor, (v) high bandwidth and fast response photodiodes are capable of hundreds of MHz bandwidth which is very useful for feedback control in high speed scanners, (vi) the whole setup is compact and low cost. The requirement for straightness of the knife edge and that it must remain at a fixed location along beam axis to maintain a constant sensitivity are limitations of this implementation.
3. Experimental measurement Experiments are set up to test the performances of both sensor implementations. Fig. 2(a) shows a block of diagram indicating the components used in the laser–photodiode experiment and is referred as Type A configuration (denoted as Type A). A laser diode driver (EK1101 from Thorlabs Inc.) energizes the diode which is, in turn, directly coupled with a fiber (FiberMax FMXL635-005). It is a single-mode fiber-pigtailed laser module provides a high fiber output power (5 mW at max.) while the fiber mode-field diameter is 4 m (FWHM is shorter than 4 m). High power light source requires low feedback resistors used in the photometric system to get the equal output compared with low power therefore reducing the time constant of the system. For the facility of setup, the end of the fiber is fixed onto a XY scanner (InsituTec IT-XY-100) having a range of 100 m in each axis. One end of a honed blade is glued on a manual micrometer stage to adjust the blade edge in x and y direction. A 3 mm PIN photodiode (FDS100 Thorlabs Inc.) operated in a biased mode (15 V) is used to measure the intensity of the laser. The photodiode was chosen for its small sensing area which reduces the noise, and it was operated in biased mode to have fast response times though the noise will be larger since the bias voltage generates a leakage current (dark current) resulting in shot noise [8]. A basic circuit with an LF411N operational amplifier was configured for transconductance with a selected feedback resistance value to provide a constant output voltage range corresponding the intensity of the LD i.e. inversely proportionate to LD power. Data acquisition system is built based on an NI LabVIEW Real-TimeTM system. Firstly turn on the laser, and tune the laser power to the required level. Adjust the feedback resistor in the circuit therefore the output of the amplifier will give an output close to 10 V to saturate the analog to digital converter (ADC). Record that value as Vfull , and then use micrometer stage to let the knife edge approach the fiber in x direction until the output reaches half of Vfull . After that, adjust the knife edge in y direction until it almost touch the fiber end, record the position as h. Finally position the XY scanner in x direction, record the position and the photodiode output and
Fig. 2. Block diagram of experimental configuration for the sensor tests. (a) Set up of LD and photodiode based knife edge sensor and (b) set up of photo-interrupter based knife edge sensor.
post-process the data. The h and power are varied for several tests in order afterwards and data are recorded respectively. Fig. 2(b) shows the similar setup for photo-interrupter experiment (denoted as Type B). The measurement circuit for the photo-interrupter contains AMP02 operational amplifier works as a differential amplifier to offset the output from the detector. An experimental evaluation of the output characteristics of both types of sensor has been undertaken. For the Type A it is necessary to measure the sensor output at different spacings between blade edge and the fiber. To avoid problems with backlash of our knife edge positioning system, in these experiments it was necessary to measure the distance from the detector, h varying from 0 mm to 3.1 mm, the latter value corresponding to the knife edge being as near to contact with the end of the fiber ferrule as was possible using the micrometer. Measurements of sensitivity and noise of this sensor were carried out at different settings of the laser power. Five levels of power at 1, 1.5, 2, 2.5 and 3 mW were tested. Sampling of the sensor output voltage was obtained at a rate of 100,000 samples per second and 1000 for measurements of noise and tracking of motion respectively. To measure the output from the sensors as a function of position of the knife edge relative to the sensor, a sinusoidal displacement x of 40 m amplitudes were used at a frequency of 0.1 Hz (Type A) and 1 Hz (Type B). For the Type B sensor, although the beam is, in principle, collimated, data at three locations along the y axis were recorded where h = 0 mm corresponded to the knife edge being centrally located between source and detector along the y axis.
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Table 2 Ranges and outputs defined by photo diode sensitivity when h varies.
Fig. 3. Stability tests of the measurement process for optical fiber displacement sensor.
h (mm)
Range (m)
Sensitivity peak (V m−1 )
90% sensitivity peak (V m−1 )
Output (V)*
1 1.5 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1
92.737 80.884 63.379 57.040 53.961 48.688 43.546 38.986 36.600 30.487 24.255 18.280 12.985 4.648
0.029 0.037 0.053 0.057 0.062 0.069 0.077 0.087 0.100 0.120 0.149 0.196 0.266 0.664
0.026 0.033 0.047 0.051 0.056 0.062 0.069 0.078 0.090 0.108 0.134 0.176 0.239 0.598
2.539 2.826 3.163 3.090 3.197 3.179 3.180 3.221 3.470 3.480 3.434 3.405 3.281 2.932
*
4. Results
Output is calculated based on the average sensitivity and range.
4.1. Stability Fig. 3 shows the output of Type A sensor data over a time period of 1 h during a time when the room temperature control was cycling approximately ±0.5 ◦ C. The experiment is set up as the knife edge sat approximately at the center of the fiber where it covered half the intensity (about 5 V at the output) corresponding to the photodiode reading half the maximum value. It contains a noise of about 10 mV PV value. The temperature of the lab recorded simultaneously shows a temperature drift which is negatively correlated to the drift of the sensor within the experimental setup. The drift is likely comes from photometric system or the thermal expansion of the devices in the metrology loop, i.e. photodiode mount or knife mount. Since the stability significantly limits the performance of the long-term measurement in changing temperature environment, a more stable environmental temperature control and better detector and circuit design with less thermal drift is required. 4.2. Dark current We vary the input laser power with corresponding gain setup and test the noise level as well the dark current noise. The results are demonstrated in Table 1. A higher illumination power level not only produces lower noise, but also enables a higher cut off frequency due to a lower gain in the photodiode circuit. The dark current noise also drops as the power goes up mainly because the feedback/load resistor is lower, and it weighs more in the total noise at the same time. 4.3. Sensor characteristic and calibration Fig. 4(a) shows the output of the photodiode (10,000 points raw data) and Fig. 4(b) shows the sensitivity (first fit the 10,000 raw data then use the derivative of the fitted equation) versus displacement of the knife edge in the x axis (see Fig. 2(a)) corresponding to different fibers to knife edge separation h at a laser power of 3 mW. From this figure the intensity looks Gaussian Table 1 Dark current noise with different power levels setup. Power (mW) Total noise Dark current (mV) 1 noise (mV) 1
Dark current/total (%)
1 1.5 2 2.5 3
8 12 20 24 26
2.356 1.477 0.906 0.693 0.655
0.193 0.172 0.182 0.167 0.172
along x axis which is the scanning direction with the sensitivity increasing as the blade approaches the fiber. It reaches to a maximum of 0.66 V m−1 where the blade almost touches the fiber (at h = 3.1 mm) and 0.02 V m−1 (at h = 0 mm) where the blade is closest to the detector. The core diameter of the fiber is 3–4 m. The reason for this trend is the Gaussian profile of the beam. Closest to the detector the beam is expanded and the detector is detecting the expanded portion of the beam. Whereas, when knife-edge is nearest to the fiber it intercepts almost the whole beam profile. Weibull function is chosen to fit the sensor displacement characteristic in Fig. 4(a). High order polynomials, Gaussian and other functions were fitted to these data sets but showed larger deviations. While the residual error for the Weibull function was lower for this function than others tried, there remained a systematic error of peak to valley amplitude of about ±6 mV. Combining a 6th order polynomial fit to these residuals it was possible reduce this to ±4 mV at h = 2.3 mm (see Fig. 4(c)). These two fitting equations only repeats when the y position (h) of the knife edge stays constant and the laser power does not change. Results of other laser power levels from 1 mW to 2.5 mW show similar characteristics. Fig. 4(b) is a plot of sensitivity with x for different separations h between the knife edge and fiber. It is reasonable to define the working range of the sensor at certain threshold values of sensitivity to provide an acceptable resolution. In this analysis, the range is defined by the translation in which the sensitivity remains within 10% of the peak sensitivity value. Table 2 shows the displacement ranges obtained at different values of h. Fig. 5(a) and (b) is respectively the output of the photointerrupter and its sensitivity versus displacement along x axis at different values of h (see Fig. 2(b)). The emitter is collimated by a lens molded into its mount. In principle, the sensitivity to motion of the blade in direction x are designed to be constant across the full 3.4 mm gap between emitter and detector of the interrupter (i.e. for different locations of h). In practice, the sensitivity reaches its maximum value at the center between the emitter and detector, while it drops when the blade is located on either side of this position. Nevertheless, the sensitivity reaches a maximum of 0.2 V m−1 . 4.4. Error sources
BW (cutoff) (Hz) 13,000 19,500 26,000 32,500 39,000
The noise sources come from the photodiode circuit, environmental temperature fluctuations and vibration, stability of the laser, blade edge roughness, and back-reflection from the surface of the blade disturbing the stability of the laser. Improper alignment of the fiber knife edge and detector will leads to coupling problems for multi-axis applications. It also
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Fig. 4. Performance of the Type A, laser diode based, displacement sensor. (a) The output of the photodiode versus displacement of the knife edge in the x axis corresponding to different fiber to knife edge separation h at a laser power of 3 mW, (b) the sensitivity of the photodiode versus displacement to different values of h at a laser power of 3 mW and (c) the fitting of the photodiode versus displacement characteristic and its residual error.
reduces the intensity coming to the detector therefore causing a decrease of the signal to noise ratio. The ambient light adds a certain amount noise to the detector. This can be avoided by covering the whole set up with an opaque
Fig. 5. Performance of the Type B, photo-interrupter based, displacement sensor. (a) The output of the photo-interrupter versus displacement of the knife edge in the x axis corresponding to different fiber to knife edge separation h and (b) the sensitivity of the photo-interrupter versus displacement to different values of h.
box, turning off the external light sources or using a band pass filter. In our test, we adapted the first two methods to limit the effect of ambient light. Temperature change will affect the knife edge’s length which mimics the sensor output. The thermal expansion coefficient of the steel (knife edge) is 11 × 10−6 C−1 , l = 0.005 m, with a temperature variations typically within 0.1 C, the systematic thermal error is about 5 nm. We prepared another block target using a silica slice with a straight line coated with aluminum. This will lower the thermal expansion to below 1 nm at the same conditions. Laser stability is another concern since there is light reflecting from the knife edge surface back into the fiber and subsequently to the laser diode. Although there is a feedback control for the diode current, this optical feedback may disturb the laser generation mechanism. By splitting a laser through an isolator and a fiber-coupler, and using one channel as a reference, the other as a measurement head, the isolator is able to attenuate the light coming back, and the instability of laser power can be solved by differential method. For calibration we used the XY positioner (InsituTec IT-XY-100) to calibrate the knife edge sensor. The linearity of the positioner is about 0.01% which corresponds to a 10 nm error at maximum position. Surface roughness of the edge will also cause deviations at the detector when the knife sensor is used in more than one axis. The photometric system noise is one main error source limiting the resolution. It is studied in the following section. 4.4.1. Configuration A The fundamental limits of the sensor system in displacement measurement come from the diode and diode driver, photo detector and photometric system and the sensitivity. In Section 4.2, the sensitivity is determined by the fiber core size (which provides a short FWHM) and the distance between the fiber core and the knife edge.
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Fig. 6. Laser diode driver supply current stability measurement.
The total noise current of the photometric system includes thermal noise ij of the shunt resistance (and channel resistance in the case of guard ring device) Rsh , the shot noise id and iph resulting from the dark current and the photocurrent, thermal noise current from the feedback resistor Rf , and amplifier noise current as expressed in Eq. (9) [8].
in
total
=
4kT 4kT 2 + 2q(id + iph ) + + iamp + (Vamp 2C)2 B Rsh Rf
(9)
where B is the noise bandwidth; k the Boltzmann’s constant, 1.38 × 10−23 (J K−1 ); T the temperature (K); q the 1.6 × 10−19 (C); id the shot current (A); iph the dark and photo current (A); iamp the amplifier input leakage current (A); Vamp the amplifier input noise voltage (V) and C is the amplifier input capacitance (F). For the photodiode used in the circuit, the NEP@650 nm is 1.5 × 10−14 W Hz−1/2 (35 MHz @20 V bias). The first two terms in Eq. (9) can be derived from NEP and the photo sensitivity [9] of the detector as 4.5 × 10−29 A2 Hz−1 . The feedback resistor Rf is about 2 k giving a value of around 10−29 A2 Hz−1 for the third term. The LF411N amplifier has 0.01 pA Hz−1/2 input noise current giving an estimated 10−28 A2 Hz−1 for the fourth term. The total current noise is 0.0124 pA Hz−1/2 which corresponds to approximately 1 V Hz−1/2 given the input impedance is around 108 . The LD driver circuit has a stability of less than 0.01% and output level of 0.1 A rms where the output current is up to 250 mA. A stability test with 3 mW laser power is shown in Fig. 6 from which an rms noise of 28 A which is at the limit of the measurement (9 A quantization noise from the 16 bits ADC) and corresponds to a stability of better than 0.02% of full scale at a bandwidth of 100 kHz. Noise data is collected when the distance h between the blade and fiber varies from near to the end of the fiber (h = 3.1 mm) to far from the fiber (h = 0 mm) while the power levels were maintained at a constant value ranging. Tests were carried out at different power levels ranging from 1 mW to 3 mW. Power spectrum measurements in Fig. 7(a) and (b) show similar distribution and magnitude over a measured bandwidth of 10 kHz for different values of h. The results show that the noise level does not change significantly with h, and the resolution was increased with reduced separation at the expense of shorter range. However, the noise spectrum values for a 3 mW source are about 1/9 to that measured with a 1 mW source. A 120 Hz and 240 Hz components are observed in the power spectrum which likely come from harmonic disturbance from the AC power lines (120 V at 60 Hz). To determine noise of the measurement system, similar measurements have been obtained with the translational stage maintained under closed loop control at a constant value of x = 50 m where the sensitivity of the sensor is at its peak. Fig. 8(a) is the power spectrum of noise when laser is controlled at different
Fig. 7. Noise level of the Type A sensor photodiode detector at different values of h. (a) Power spectrums of noise when the laser power is 1 mW and (b) power spectrums of noise when the laser power is 3 mW. Note that the range of the vertical scales (9 mV2 at 1 mW and 1 mV2 at 3 mW laser power) in proportion to the inverse square of the laser power.
power levels. It shows that the lower the power level, the higher of the noise level, a result again correlating with the inverse relationship between amplifier gain and laser power. It can be observed that the noise distribution exhibits a 1/f characteristic below about 1 kHz. Fig. 8(b) shows the cumulative power spectrum of noise as the laser power varies. Noise density is about 7.45 V Hz−1/2 at 1 mW laser power and 2.08 V Hz−1/2 at 3 mW which would correspond respectively to an rms noise of around 0.668 mV and 0.245 mV at a bandwidth of 1 kHz. With the sensitivity (at maximum point or x = 50 m) of 0.664 V m−1 at 3 mW power level and h = 3.1 mm, the displacement noise corresponds to around 0.37 nm, again at a bandwidth of 1 kHz. The SNR is about 40,000 for 3 mW and is 15,000 for 1 mW at 1 kHz bandwidth. Ignoring the 1/f at lower frequencies, the SNR will be higher. 4.4.2. Configuration B Photo-interrupter noise level data has been collected while the location of the blade along the optical axis (y axis) varies. As shown in Fig. 9, the power spectrum with the knife edge at different locations is little changed. A considerably larger 60 Hz AC power frequency and its odd harmonics appear in the spectrum (60 Hz, 180 Hz, and 300 Hz). This corresponds to about 60–70% of the total noise power. The noise density is about 74.1 V Hz−1/2 which would give an rms noise of around 7.4 mV corresponding to 37 nm with a sensitivity of 0.2 V m−1 at a bandwidth of 10 kHz and SNR of
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Fig. 8. Noise level of the photodiode when the laser power varies. (a) Power spectrums of noise with different laser powers and (b) cumulative power spectrums of noise with different laser powers.
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Fig. 10. Experimental setup for tuning fork characteristics measurement using optical fiber displacement sensor. Fig. 9. Power spectrums of the photo-interrupter noise at different values of h.
around 2700. In the absence of this 60 Hz spike, the cumulative power spectrum will drop down to around 9 mV2 and the rms noise will be in the region of 3 mV corresponding to an rms displacement noise of 14 nm and a corresponding SNR of better than 8000. The AC spike may come from unfiltered power used as a reference voltage and unshielded electrics. 4.5. Application: measuring tuning fork oscillation To evaluate the dynamic response, resolution, accuracy of the optical sensor, we applied this method to measure the dynamic as well as the amplitude of a tuning fork oscillator. Optical methods have been used to measure the absolute mechanical vibration amplitude and phase of the tuning fork for calibration and displacement sensitivity, i.e. a homodyne interferometer [10], and differential interferometry [11]. Ruiter et al. [12] measured the amplitude by gluing a fiber to one arm of the fork. Though being relatively easier to setup than an interferometric system, this method adds mass and stiffness to the fork that will, in turn, have a significant influence on its response. In this study, to demonstrate the high bandwidth and resolution of this optical fiber displacement sensor, the amplitude of tuning fork has been measured by using one arm of the fork as the knife edge to block light to the photo detector. The output (V) of the detector is calibrated to displacement using the nano-positioning XY scanner (InsituTec IT-XY-100) in a similar way in Section 4.3 where the knife edge is replaced by the tuning fork tine here. Fig. 10 shows the tuning fork attached to the XY scanner that is used to calibrate photodiode output voltage. Firstly the XY scanner is hold at a home position, and a sine wave voltage of amplitude 0.1 V is fed into the tuning fork directly using a signal generator (Tektronix AFG 3022B). The light intensity variation caused by the tine oscillation in y direction of the fork is measured by the photodiode. Then to calibrate the output of the photodiode, the stage of the XY scanner was translated in the y direction with an amplitude of 600 nm at a frequency of 1 Hz to block the light, where the fork tine is stationary. This calibration gives an rms value of 1.2 nm at 3.50 MHz bandwidth. Resolution is increased to 0.6 nm at 30 kHz and, assuming constant spectral density, 30 pm at 1 Hz bandwidth. For commercial displacement measurement interferometer or high resolution capacitance sensor, the resolution is about nanometer at couple kilohertz. This method provides a high resolution and bandwidth measurement with a limited range which is beneficial for specific applications where the dynamic displacement measurement is required.
By using the calibration information, Fig. 11(a) shows a time history of tuning fork oscillation at its resonant frequency of 32,752.36 Hz with a drive voltage of amplitude 0.1 V measured with a sampling rate of 300 ksps. A least square fitting yields an estimated amplitude of 265 nm. The standard deviation of the fitting error is 6.1 nm for about 5 periods data leading to an SNR of 31. Fig. 11(b) shows a time period data at the resonant frequency using self-sensing method from the piezoelectric signal. The of the fitting error is 0.027 V for about 4000 point data leading to an SNR of 24. The static amplitude has been measured by following two different methods. Fig. 12(a) shows the oscillation at 10 Hz with a drive voltage of amplitude 10 V (it was not possible to detect any measurable signal with a drive voltage of amplitude 0.1 V)with a sampling rate of 10 ksps and its fit. A 120 Hz oscillation of around 2 nm PV is observed to be superposed onto this 10 Hz signal that is interference from laboratory power lines. A least square fitting yields an estimated amplitude of 3.2 nm. The standard deviation of
Fig. 11. Tuning fork amplitude measurements comparison at resonant frequency. (a) Using the optical fiber displacement sensor and (b) using the self-sensing method from the piezoelectric signal.
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5. Conclusion This novel sensor based on the principle of photo-interrupter and knife edge does not require complex signal conditioning circuit while maintaining a high SNR at reasonable bandwidth. The relatively small number of components and the fact that all can be made using microelectronic processing technology makes it possible to produce a measurement system having a small footprint. Its low cost, low mass and compact size are desirable attributes for a nonintrusive, precision displacement sensor. Sensitivity goes up and the noise density remained relatively constant under the conditions of constant optical power level, reduced separation between the knife edge and source. In these measurements, it has been demonstrated that nanometer resolution in displacement measurement can be relatively easily obtained by placing knife edge close to the fiber having a core diameter of around 4 m. The tuning fork measurement demonstrates the optical sensor’s high dynamic response with MHz bandwidth at nanometer resolution. Further study is necessary to investigate how the quality of blade edge influences the performance. References
Fig. 12. Tuning fork amplitude measurements comparison at 10 Hz. (a) Using the optical fiber displacement sensor and (b) using the self-sensing method from the piezoelectric signal.
the fitting error is 1 nm for about 4 periods of data resulting in an SNR of 2 after removing the 120 Hz background noise. Fig. 12(b) shows time period data of tuning fork with the same driving signal using self-sensing method. The fitting signal’s amplitude is 0.005 V when the background noise is removed, and the standard deviation of the fitting error is 0.003 V for 5 periods data resulting in an SNR of 1. To validate this ‘static’ measurement, a stylus profiler (Rank Taylor Hobson Talystep) was also used as a second method to directly measure displacement of the tuning fork when driven at 10 V amplitude at 1 Hz for which an amplitude and standard deviation of 3.28 ± 0.2 nm was observed. The above two comparisons show that the optical knife-edge method’s SNR is twice that of the self-sensing method for amplitude measurement far from resonance. At or near the resonance of the tuning fork, the SNR of optical knife-edge methods is 30% higher than the self-sensing method.
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