Sinusoidal fringe projection system based on compact and non-mechanical scanning low-coherence Michelson interferometer for three-dimensional shape measurement

Optics Communications 282 (2009) 1237–1242

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Sinusoidal fringe projection system based on compact and non-mechanical scanning low-coherence Michelson interferometer for three-dimensional shape measurement Tulsi Anna a, Satish Kumar Dubey b, Chandra Shakher a, Amitava Roy c, Dalip Singh Mehta a,* a

Laser Applications and Holography Laboratory, Instrument Design Development Centre, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110 016, India Central Scientific Instruments Organization, Chandigarh 160030, India c SERC Division, Department of Science and Technology, New Delhi, India b

a r t i c l e

i n f o

Article history: Received 18 June 2008 Received in revised form 12 November 2008 Accepted 14 November 2008

a b s t r a c t We report a sinusoidal fringe projection system based on superluminiscent diode (SLD) as a broad-band light source in conjunction with an acousto-optic tunable filter (AOTF) as frequency tuning device for three-dimensional shape measurement. The present system is based on a compact low-coherence Michelson interferometer system. The conventional interferometric system was modified in which one side of the beam splitter was coated with aluminum oxide which is used as reference mirror. With this modified version, interference fringes can easily be obtained by simply placing the external mirror in contact on the other side of beam splitter. Sinusoidal fringes with multiple spatial-carrier frequency can be generated in real-time using the present system by means of changing the radio-frequency signal to AOTF electronically without mechanically moving any component in the system. The present system was tested by projecting the sinusoidal fringes on a step-like object and 3D shape of the object was reconstructed using Fourier transform fringe analysis technique. The main advantages of the proposed system are completely non-mechanical scanning, easy to align, high stability because of its nearly common-path geometry and compactness. Ó 2008 Elsevier B.V. All rights reserved.

1. Introduction During the last three-decades various non-contact and non-destructive techniques have been developed for measuring three-dimensional (3D) shapes of discontinuous objects. Threedimensional shape measurement based on optical techniques have been very successful because they are non-contact and nondestructive, fast and accurate. Optical non-contact profilometry has been widely used for 3D sensing, mechanical engineering, machine vision, intelligent robot control, industrial monitoring, accurate stress/strain and vibration measurement, etc. [1–3]. One of the most important technique is 3D sensing by coherence radar [4], in which the low-temporal coherence of light source is exploited. Three-dimensional shape of the object is reconstructed from the measurement of the peak of the high-visibility fringes by means of scanning the object in X–Y–Z directions. On the other hand the most commonly used optical methods for 3D shape measurement include structured light projection [3,5], moiré interferometry [3,6,7], 3D topometry by stereo microscopy [8], photogrammetry [9], digital fringe projection [10–13], single-, dual- and multiplefrequency and color grating projection [14–17], digital micro-mir* Corresponding author. Tel.: +91 11 2659 1865; fax: +91 11 2658 6729. E-mail address: [email protected] (D.S. Mehta). 0030-4018/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2008.11.080

ror devices [18,19], liquid crystal display projection [20–23], and color-coded fringe projection [24]. Basically all these techniques follow the same principle i.e., the inspected surface is illuminated by a periodic pattern from the projection system and distorted pattern due to surface discontinuity is recorded by the image acquisition system at a different viewpoint [25]. A number of fringe pattern analysis methods for analyzing deformed fringe patterns including Fourier transform profilometry (FTP) [2,26–30], phaseshifting profilometry (PSP) [31–33], spatial phase detection (SPD) [34], phase demodulation method [35] and also shearography [36]. These techniques are highly accurate and efficient and can be used in robust environment. One of the key devices used in these techniques is the efficient generation of periodic patterns with changes in the spatial and temporal carrier frequency and also with phase-shifting patterns in real-time. In case of multiple-frequency gratings projection systems [15,16,27] the disadvantage is that, once the gratings are fabricated one cannot change the spatial-carrier frequency of the grating in real-time. Further, realization of high-quality dual or multiple-frequency sinusoidal gratings requires special techniques to fabricate them and these systems are expensive. Interferometric fringe projection is an alternative technique for generating pure sinusoidal fringes with multiple spatial-carrier frequency in real-time. Various interferometric fringe projection techniques have been

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developed during the past few years. Lateral shearing interferometer [37], superluminescent diode interferometer with sinusoidal phase modulation [38], interferometric fringe projection system [39], composite interferometer [40] and conventional Michelson interferometer [41] have been investigated for 3D shape and step-profile measurement. Apart from these, the interferometeric systems based on acousto-optic demodulator (AOM) [42], dual acousto-optic deflection encoding (D-AODE) [43,44] and an acousto-optic grating based fringe projector [45] have also been developed. But these systems are complicated and require careful adjustment to obtain the interference fringes. Further, 3D shape measurement systems based on interferometric fringe projection, such as, conventional Michelson interferometer configuration are highly sensitive to the external vibrations and thus can not be used in robust environment. Recently, a almost common-path shearographic interferometer using the separation of the polarization states and for digital phase-shifting shearography has been developed [46,47]. This shearing device having the advantage common path, low cost and also low sensitive to external disturbances but uses a high power source i. e., Nd-YAG laser and high-speed CMOS camera and such lasers are bulky and costly. Further, a stable and simple multi-frequency and phase-shifting fringe projection system based on two-wavelength lateral shearing interferometry for three-dimensional profilometry [48], and a wavelength scanning Talbot effect for 3D step-height measurement [49] have been developed. But it is difficult to produce interference fringes in a shear interferometer using a low-coherence light source because shear plates are quite thick and the optical path difference between the two beams (one reflected from the front surface and other from the back surface) is much larger than the coherence length of the broad-band source. More recently, a compact Michelson interferometer system was designed and developed for swept-source optical coherence tomography (SS-OCT) for finger print detection [50]. In both the studies, i.e., for wavelength scanning Talbot effect [49] and in SS-OCT a unique combination of superluminiscent diode (SLD), an acousto-optic tunable filter (AOTF) as frequency-tunable light source have been used. In this paper, we report the generation of multi-frequency spatial-carrier sinusoidal fringes for 3D shape measurement using a compact and non-mechanical scanning low-coherence Michelson interferometer in conjunction with SLD as broad-band light source and AOTF as frequency tuning device. To make the system compact and handy, conventional interferometric system was modified by coating aluminum oxide on one side of cube beam splitter, which acts as a fixed reference mirror. With the modified version, interference fringes can be obtained easily by placing the external mirror on the other side of beam splitter. From this set-up a variety of sinusoidal fringe patterns were generated, i.e., we obtained changes in the spatial-carrier frequency of the fringes either by changing the radio-frequency (RF) signal to AOTF or changing the angle of external mirror at fixed RF frequency to AOTF. One of the main advantages of the multi-frequency fringe projection system is that it provides an appropriate and more-accurate phaseunwrapping mechanism for objects with large discontinuities. The generated sinusoidal fringes were then projected on the 3D object and distorted fringes were recorded by detector. Three-dimensional shape of the discontinuous object was then reconstructed Fourier transform fringe analysis technique. As compare to other techniques for generating fringe patterns, the present sinusoidal fringe projection system is based on compact low-coherence Michelson interferometer and has many advantages. It is nearly a common-path interferometer, hence is insensitive to external vibrations, and is compact in size. It can generate multiple spatial-carrier frequency of fringes in real-time by means of changing the RF signal to AOTF electronically without moving any component mechanically. One of the major advantages of the present sys-

tem is that because of the low-coherence nature of fringe projection system no spurious fringes are obtained due to multiple reflections from the surfaces of optical components. Such spurious fringes are often obtained in the case of laser based fringe projection systems due to long coherence length of the light source and such spurious fringes has to be removed before processing the data. Because of these advantages this technique is suitable for industrial applications in robust environments. 2. Principle of the sinusoidal fringe projection system In grating projection profilometry one cannot change the spatial-carrier frequency of the grating in real-time [15,16]. For changing the carrier frequency one has to physically replace the grating during the experiment and mechanically move the grating for generating phase-shifting patterns. In case of interferometric fringe projection system one can change the carrier frequency in real-time but these systems are based on conventional Michelson-interferometric configuration [34,41,42]. These interferometers require careful adjustment of two independent mirrors to equalize the optical path-length and obtain interference fringes. We have designed a compact and nearly common-path sinusoidal fringe projection system as shown in Fig. 1. In order to avoid tedious and time-consuming reference mirror adjustment, we coated one side of the 40–60 cube beam splitter (BS), dimension 16 mm  16 mm  16 mm with aluminum oxide. Coated surface of the BS works as a fixed reference mirror and uncoated side is used for another mirror. An external mirror was placed very close to the uncoated side of the BS. This arrangement makes sure that the optical path difference between the two mirrors nearly equal and which remains always within the coherence length of the light source and the interference fringes can be easily obtained with this system. With this modification, present sinusoidal fringe projection system becomes very compact and nearly common-path. Further, this system can generate multiple spatial-carrier frequency of fringes in real-time by means of changing the RF to AOTF electronically or changing the angle of the external mirror. The generated fringe pattern g(x, y; k) can be expressed by the following equation [48]

gðx; y; kÞ ¼ Sðx; y; kÞ½1 þ cðx; y; kÞ cosf2pfo x þ D/ðx; y; kÞg

ð1Þ

where S(x, y; k), c(x, y; k), fo and D/(x, y; k) are the spectral amplitude, correlation function, spatial-carrier frequency and phase difference of the fringe pattern, respectively. The phase difference of the fringe pattern can be written as

D/ðx; y; kÞ ¼

2p Dpðx; y; kÞ k

ð2Þ

where Dp is the optical path difference between the two interfering beams, k is the wavelength of light and it can be expressed as [51]

Dp ¼ 2nd cos h 

k 2

ð3Þ

where ‘n’ and ‘d’ are the refractive index in the air and geometrical path-length, respectively. From Eqs. (1)–(3) it can be seen that for a fixed angle h the number of interference fringes changes upon changing the k of light [51]. On the other hand the number of fringes can also be changed by changing angle h at a fixed k. Hence, the spatial-carrier frequency of the fringes can be varied by changing the wavelength k of the input light source electronically using a combination of SLD and AOTF without mechanically moving any component in the set-up. For a particular wavelength k the generated fringe pattern can be expressed as [48]

gðx; yÞ ¼ aðx; yÞ þ bðx; yÞ cosf2pfo x þ /ðx; yÞg

ð4Þ

where a(x, y), b(x, y) are the DC-component and fringe amplitude. Fourier transform of each fringe pattern can be computed and one

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Fig. 1. Schematic diagram of sinusoidal fringe projection profilometric system for three-dimensional shape measurement.

of the spatial-carrier spectrum filtered and inverse Fourier transformed to obtain the analytical signal

cðx; yÞ ¼

bðx; yÞ expfi½2pfo x þ /ðx; yÞg 2

ð5Þ

The experimental details of the low-coherence sinusoidal fringe projection system are given below. 3. Experimental details Fig. 1 shows the proposed sinusoidal fringe projection profilometric system comprising a frequency-tuned light source system. It is the combination of a superluminiscent diode (SLD) (Model No. SLD-371-HP1-DIL-PM-PD, SUPERLUM Diodes Ltd.) and an AOTF (NEOS Technologies, Inc., USA) that turns into completely non-mechanical scanning in nature. Broadband light emitting from SLD was coupled into the input of AOTF through a polarization maintaining single mode optical fiber using an FC connector. The spectral characterization of SLD with high resolution spectrometer (HR 4000 Ocean Optics Ltd.) gives two peaks at 819.55 and 845.82 nm with spectral full-width at half maximum

a

800 810 820 830 840 850 860 870 880 890 900 1.0

(FWHM) of 48.38 nm. At the input current of 174 mA (temperature 25 °C), the peak power of SLD is 7.5 mW. The measured spectrum of SLD is shown by Fig. 2a. AOTF has high speed of operation of the order of a few microseconds, large tunability range 600–1200 nm with RF-frequency range 60–132 MHz. These are solid-state electronically tunable optical filters that select precise wavelengths by applying appropriate RF and hence mechanically moving parts are not required. Application of RF to AOTF transducer controls the transmitted wavelength. The RF-frequency was changed linearly with a constant step of 0.1 MHz from 87 to 95 MHz and the tuned spectrum was recorded using spectrometer. Observation reveals a linear relationship between RF-frequency and peak wavelength and was observed that for every 0.1 MHz shift in the input frequency, peak of the tuned spectrum is shifted by 0.75 nm. The characterization of AOTF is also made by using a spectrometer. It was observed that the spectral line width (dk) of the frequency-tuned AOTF spectrum remains same throughout the sweeping width of 0.75  81 nm and is found to be 1.5 nm. Assuming the SLD and AOTF tuned spectrum nearly Gaussian, we calculated the coherence length lc, by the formula

b 12000 11000

1.0

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

9000

Intensity (Arb.Units)

Intensity (Arb.Units)

10000 8000 7000 6000 5000 4000 3000 2000 1000 0.0 0.0 800 810 820 830 840 850 860 870 880 890 900

Wavelength (nm)

0 800

810

820

830

840

850

Wavelength (nm)

Fig. 2. (a) Spectral distribution of low-coherence light source. (b) Filtered spectra of AOTF at different RFs.

860

870

880

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a

d

250 200

Intensity (Arb.Units)

Intensity (Arb.Units)

c

b

150 100 50

250

200

150

100

50 0 0

50

100

150

200

0

50

Pixels

100

150

200

Pixels

Fig. 3. (a) and (b) show the example of recorded interferograms at fixed RF to AOTF 89.6 MHz at different angles of external mirror; (c) and (d) are the corresponding sinusoidal intensity profiles.

lc ¼

4 ln 2 k20 p Dk

ð6Þ

where k0 is the central wavelength and Dk spectral full-width at half maximum. Substituting Dk = 48.38 nm and k0 = 842.5 nm for SLD in Eq. (6), lc turns out to be 12.954 lm. The axial resolution depends upon the FWHM of source spectrum, i.e., SLD only and since the axial resolution is the half of the coherence length hence comes out to be 6.5 lm. Similarly lc of tuned spectrum from AOTF was calculated by putting spectral linewidth dk = 1.5 nm and k0 = 842.5 in Eq. (6) which turns out to be 0.418 mm. The tuned spectrum at different RF-frequencies applied to AOTF is shown in Fig. 2b. Thus we obtain a fine-tuned spatially coherent but temporally low-coherent light at the output of the AOTF. Therefore, the present system works on the principle of low-coherence interferometry. The spatial-carrier frequency was varied significantly within the coherence length of the tuned light, i.e. 0.418 mm. As mentioned in the theory the spatial-carrier frequency can also be varied by changing the tilt angle of the interferometer. For a compact interferometer system the coherence length is sufficient to produce spatial frequencies up to several l p/mm. One promising development in AOTFs is that they are already commercially available. Thus by scanning the wavelength of the broad-band light from SLD using AOTF, a frequencytunable low-coherence source for sinusoidal fringe projection was realized. Because of the low-coherence nature of fringe projection system no spurious fringes are obtained due to multiple reflections from the surfaces of optical components and object under study. The beam from frequency tunable source was collimated by using collimating lens L1. The collimated beam was then made incident into the compact modified Michelson interferometer. Interference fringes can easily be obtained by simply placing the

mirror in contact on the other side of beam splitter, and the system generates spatial-carrier fringe patterns by means of changing the RF signal to AOTF. It was tuned sequentially with a constant step of 0.1 MHz from 87 to 95 MHz. Hence, pure sinusoidal fringes can be generated with the present system. The spatial-carrier frequency is increased either by changing the angle between the two mirrors manually or changing RF signal to AOTF. The sinusoidal fringes with multi-frequency were recorded by a CCD detector (Roper Scientific, Inc.) having 1392  1024 pixels with each pixel size 6.5 lm  6.5 lm). 4. Results and discussion Interferograms were recorded by CCD detector and analyzed by MATLAB software. Fig. 3a and b shows the examples of recorded interferograms at fixed RF 89.6 MHz by slightly changing the angle of the external mirror. Fig. 3c and d are the corresponding sinusoidal intensity profiles, respectively. From these Figures it can be seen that good contrast of interference fringes were obtained and the line profile is also pure sinusoidal. Fig. 4a and b shows the recorded interferograms at different RF applied to AOTF, i.e., at 87.3 MHz and 94.9 MHz, respectively. The corresponding sinusoidal intensity profile is shown in Fig. 4c and d, respectively. Hence, we could generate variety of sinusoidal fringe patterns from the present non-mechanical scanning, compact low-coherence interferometric system. The present system was tested by projecting sinusoidal fringe patterns on a three-dimensional discontinuous step-like object with the help of projection lens L2. The step was made of a machined aluminum rough object. The object was imaged by a camera

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a

b

c

d Intensity (Arb.Units)

Intensity (Arb.Units)

250 200 150 100

250 200 150 100 50

50 0

0

50

100

150

200

Pixels

0

50

100

150

200

Pixels

Fig. 4. (a) and (b) show the recorded interferogram at different RF applied to AOTF 87.3 and 94.9 MHz, respectively and (c) and (d) are corresponding sinusoidal intensity profiles.

zoom lens with variable focal length, which was kept in front of the CCD camera. Originally the collimated beam size which is made incident on the interferometer is 5 mm  5 mm and the spatial frequency at the output of the interferometer is about 2–3 lp/mm. After generating the sinusoidal interference fringes they are passed through a projection lens (zoom lens) then the area of projection (field width) is increased and was about 20 mm  20 mm. The area

of fringe projection can be increased further by changing the zoom lens. Distorted fringe patterns reflected from object were recorded sequentially by tuning the RF-frequency to the AOTF with a constant step of 0.5 MHz over the entire wavelength range using a CCD detector. The photograph of scanned object is shown by Fig. 5a and a black box on this indicates that area which is being projected. Fig. 5b shows an example of a distorted interference

Fig. 5. (a) Photograph of the scanned object, (b) deformed fringe patterns on the step-like object, and (c) reconstructed 3D shape of the object.

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fringe projected onto the object at 91.0 MHz RF applied to AOTF. The distorted fringe patterns recorded by CCD camera were analyzed by using Fourier transform fringe analysis technique. In Fourier transform technique, the Fourier transform of both the reference and object 2D images were computed and the first order of the Fourier spectrum was selected and filtered. Then inverse Fourier transform was performed. The obtained wrapped phase map of reference and object 2D images were then unwrapped. The 3D shape of the object was then reconstructed by subtracting the unwrapped phase maps and shown by Fig. 5c. Although the present system can generate multiple interferograms by means changing the wavelength of light, but we have used single interferogram projected on discontinuous object and on the reference surface. The resolution of the present system depends upon the focusing condition and pixel size of CCD camera and the accuracy in the measurement of phase. The present system can also generate phase-shifted interferograms by means of changing the RF-frequency to AOTF in small steps. With the help of phase-shifting technology the vertical resolution of the system can be very high. Detailed analysis of multiple interferograms simultaneously and phase-shifting technique is being investigated to reconstruct the 3D shape of the microstructures and the same will be reported elsewhere. One of the major advantages of the present system is that no spurious fringes are obtained due to multiple reflections from the surfaces of optical components used in the system because of low-coherence light source system being used. Such spurious fringes are often obtained in the case of laser based fringe projection system due to long coherence length of the light source and the spurious fringes has to be removed before processing the data. The present AOTF has high speed of operation of the order of a few microseconds, large range of tunability, and linear wavenumber-RF-frequency characteristics. However, the system’s response time is limited by the CCD frame rate as we have used a low frame rate CCD camera in the present system. For the future modifications in the system one can use a high-speed CMOS/CCD camera having the same speed as that of AOTF and hence the system can be synchronized accordingly and can be made faster as compared to mechanically moving parts. With the help of high-speed CCD/ CMOS camera in conjunction with present AOTF the system can generate very fast sinusoidal fringes and hence can be useful for 3D shape measurement of objects in real-time. Further, it can also generate variety of fringes, such as, phase-shifted interferograms, and multiple spatial-carrier frequency by means of simply changing the wavelength of light by AOTF electronically. Such a system can be useful for 3D shape measurement in real-time.

interferometry, easy for alignment, high stability because of its nearly common-path geometry and compactness.

5. Conclusion

[43]

We have developed and demonstrated a nearly common-path, compact and non-mechanical scanning sinusoidal fringe projection system for 3D shape measurement using SLD in conjunction with AOTF. In this modified version of Michelson interferometer, the fringes can easily be obtained by simply placing an external mirror in contact on the other side of BS. This present system can generate multiple spatial-carrier frequency of fringes in real-time by means of changing the RF to AOTF electronically or by means of changing angle of the external mirror. The main advantages of the proposed system are completely non-mechanical scanning, low-coherence

[44]

Acknowledgement Authors gratefully acknowledge the financial assistance from Department of Science and Technology, Delhi, Government of India for the Project No. SR/S2/LOP-02/2003. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42]

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