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High-resolution knife-edge laser beam profiling
15 January 1997
OPTICS COMMUNICATIONS ELSEVIER
Optics Communications
134 (1997) 21-24
High-resolution knife-edge laser beam profiling W. Plass, R. Maestle, K. Wittig, A. Voss, A. Giesen Instirutjiir
Struhlwerkzeuge.
Received 29
Uniuersitiit
Stutfpri,
Stuttput.
Germuny
April 1996;accepted2 August 1996
Abstract A knife-edge method for profiling focused and unfocused laser beams with a high spatial resolution is presented. High resolution is achieved by dithering the knife-edge in the scan direction. The method is equivalent to the slit method but with a variable slit width also on a sub-pm scale. A signal-to-noise ratio of IO6 : 1 has been demonstrated. The design is nearly as simple and of low-cost as that of the conventional knife-edge method. The inversion algorithm used for obtaining the beam profiles from knife-edge data is discussed. An excellent agreement is found between measured and calculated beam profiles. The accuracy of this method is demonstrated also with beam propagation measurements.
1. Introduction The knife-edge method for measuring the spatial profile of a laser beam [ 1,2] has been in use since the invention of the laser itself. Despite the availability of very comfortable camera based beam-profiling systems and the fact, that this method is limited to radially or at least elliptically symmetric beams, it is still used today [3-51. One reason is the high spatial resolution, which is only restricted by the resolution of the mechanical stages (< 1 Km). Especially in micromachining, with focal spots of several 10 pm, beam profile measurements are possible with a simple setup and with high accuracy. The simple and low-cost design makes this method available for most users. In contrast to the pin-hole or camera based methods, when using the knife-edge method, the beam profile is obtained only after differentiating and subsequently transforming the data. The differentiation reduces considerably the signal-to-noise ratio of the 0030418/97/S17.00 PII
calculated profile. A differentiation is not necessary if the data are obtained with the slit method, but slit width smaller than a few p,rn are difficult to produce. The improved method presented here combines the advantages of both the conventional knife-edge method and the slit method. The data are obtained by dithering the slowly moving knife-edge, which makes this method equivalent to the slit method. Using a lock-in amplifier, the modulated part of the beam (the ‘slit’) can be detected. The ‘slit width’ can be varied on a km to sub-km scale by controlling the amplitude of the dither movement. The applicability of this method is demonstrated by measuring the far-field diffraction pattern of a circular aperture at the focus of a lens and comparing it to the theoretical profile. Beam propagation measurements based on the new knife-edge method and on a CCD-camera are also presented. The algorithm that we found most useful for transforming the data, is discussed.
Copyright 0 1997 Elsevier Science B.V. All rights reserved.
SOO30-4018(96)00527-5
W. Pluss er al. / Optics Communicarions
22
2. Transformation
algorithm
The algorithm used for transforming the knifeedge data to a beam profile is related to the geometry depicted in Fig. 1. With a sufficiently small sample spacing a, the intensity at the position rj can be assumed to be a constant Ii within the area Aij and can be calculated from the signals Pi, measured at the positions xi. From Fig. 1, it is clear that each Pi is a weighted sum of Zj, where the weighting factors are given by the areas Aij:
(1) Therefore, the transformation from Pi to Z, is a linear equation: Ij= f &A,,‘P,.
(2)
I
areas Aii and Aij can be calculated by a two-dimensional integration according to
The
Aii
[~a;~6+u’2”“i
=
dy
(3)
dx
I
and
(4) respectively. The transformation given in Eq. (2) obviously does not include any smoothing, which is sometimes
1
F-2 Pl
done with data obtained with the conventional knife-edge method [l]. Note, that the signals of the conventional knifeedge method Pconv,i are related to the signals Pi by ‘i
=
‘c0nv.i
-
‘conv.i-
3. Experimental
Y
t x- moving direction
moving knife edge
Fig. 1. Geometric
illustration
of transformation
algorithm.
(5)
I’
realization
The typical set-up used for knife-edge measurements is shown in Fig. 2. A reference measurement was employed to account for laser power fluctuations. Both, the scan and the reference signals were measured using an integrating sphere to improve the accuracy of this method. A digital lock-in amplifier (Stanford Research Systems SRS 850) detected the modulated signal at the dithering frequency of the knife-edge. The enlarged view in Fig. 2 shows the schematic drawing of the dithering knife-edge. The dither movement of the razor-blade and its lever, which is mounted with a leaf spring, can be achieved by applying a low ac voltage to the piezoelectric transducer. For a sinusoidal voltage, the oscillation of the razor blade is also sinusoidal in scan direction. The oscillation frequency was chosen to be the mechanical resonance frequency (217 Hz) of the lever, because the amplitude was most stable in this case. The oscillation frequency determines the minimum time constant of the lock-in amplifier and subsequently the measurement time, which was about one minute for a resolution of 100 points/scan.
4. Measurements methods
2t Pi
I34 (1997) 21-24
and
comparison
with
other
The advantage of the dithering knife-edge method compared to the conventional knife-edge method is demonstrated in Fig. 3, where the beam profile of an unfocused He-Ne laser beam is shown, as measured using the two methods. The enhanced signal-to-noise ratio of the dithering knife-edge is clearly visible. In fact, the signal-to-noise ratio of the used detectorlock-in-amplifier combination, which is about lo6 : 1, is maintained in the beam profile. The accuracy of this knife-edge method was tested by comparing a measured and calculated profile of a
W. Plass et al./Optics
Beam-splitter
Communications
23
134 (1997) 21-24
Laser
integrating sphere Knite-edge
Razor blade
Piezo-transducer Leaf spring
Fig. 2. Scheme of experimental
set-up.
He-Ne laser beam (diameter 2.5 mm, 0 < 1 mrad) in the far-field of a 0.9 mm aperture. The far-field profile was measured in the focal plane of a lens (f= 30 mm). An excellent correspondence can be observed, see Fig. 4. Scanning such a profile with a pin-hole is a difficult task because the position of the minima depends critically on the positioning of the pin-hole with respect to the center of the laser beam, whereas the measured intensity at the minima is too high if the aperture of the pin-hole is too large. For an investigation and theoretical discussion of laser beam propagation, beam width measurements are often useful and necessary [2,6,7]. Beam width data obtained with the dithering knife-edge method have therefore been compared to data obtained by a low-noise liquid-nitrogen cooled CCD camera (Astromed LNC, S/N-ratio: 3 X 104/1; 16 bit resolution). The measurements were done along the propagation axis of a He-Ne laser beam. Fig. 5 depicts the beam widths, measured with both methods according to the second-moment definition. Both methods agree
Fig. 4. Far-field profile of a He-Ne laser beam, diameter 2.5 mm, aperture diameter 0.9 mm, in the focal plane of a lens, f’= 30 mm, as measured by the dithering tmife-edge method and calculated analytically.
well with each other. Here the low signal-to-noise ratio of the dithering knife edge is especially important, as the second-moment definition of the beam diameter is very sensitive to a noisy signal.
5. Conclusions The dithering knife-edge is a new method for beam profiling with high accuracy and high spatial resolution. The spatial resolution can be extended far below the sub-p.m level. Unlike the conventional knife-edge method, the dithering knife-edge yields the same signal-to-noise ratio for the beam profile that can be realized with the detector-lock-in-amplifier combination. Hence, the transformation algorithm used for obtaining the beam profile from knife-edge data does not need to smooth the data. An
1
0
Fig. 3. Beam profile knife-edge.
measured
with conventional
and dithering
IO
Irn
1m
35.3
C?CQ&LlzWl, oshn2a.g
4w
A50
Fig. 5. Knife-edge and camera based 2nd-moment beam width measurements along the propagation axis. For comparison, the measurements are referenced to each other.
24
W. Pluss et d/Optics
Communications
excellent agreement could be achieved in a comparison of measured and calculated focused-beam profiles. For determining beam diameters, the dithering knife-edge method also agrees well with measurements obtained by a high resolution CCD camera.
Acknowledgements
This work was partly supported by the Bundesministerium fur Forschung und Technologie under Contract 13 N 5809.
134 (1997) 21-24
References [I] R.M. O’Connell and R.A. Vogel, Simple accurate inversion of knife edge data from radially symmetric laser beams, in: Laser Induced Damage in Optical Materials 1985, NBS, Spec. Publ. 746 (1988). [2] D.R. Skinner and R.E. Whitcher, J. Phys E 5 (1972). [3] R.M. Wood, Laser Damage in Optical Materials (Adam Hilger, Bristol-Boston, 1986). [41 A.E. Siegmamr, M.W. Sasnett and T.F. Johnson, IEEE J. Quantum Electron. 27 (4) (1991) 1098. [s] J. Hue, J. Dijon and P. Lyan, in: Laser Induced Damage in Optical Materials 1992, SPIE Vol. 1848 (1993) p. 125. (61 K. Wittig, R. Maestle and A. Giesen, in: Beam Control, Diagnostics, Standards and Propagation, 1995, SPIE Vol. 2375 (1995) p. 306. 171 ISO/DIS I1 146, Test methods for laser beam parameters, beam widths, divergence angle and laser beam propagation factor, ISO, The International Organization for Standardization ( 1995).
OPTICS COMMUNICATIONS ELSEVIER
Optics Communications
134 (1997) 21-24
High-resolution knife-edge laser beam profiling W. Plass, R. Maestle, K. Wittig, A. Voss, A. Giesen Instirutjiir
Struhlwerkzeuge.
Received 29
Uniuersitiit
Stutfpri,
Stuttput.
Germuny
April 1996;accepted2 August 1996
Abstract A knife-edge method for profiling focused and unfocused laser beams with a high spatial resolution is presented. High resolution is achieved by dithering the knife-edge in the scan direction. The method is equivalent to the slit method but with a variable slit width also on a sub-pm scale. A signal-to-noise ratio of IO6 : 1 has been demonstrated. The design is nearly as simple and of low-cost as that of the conventional knife-edge method. The inversion algorithm used for obtaining the beam profiles from knife-edge data is discussed. An excellent agreement is found between measured and calculated beam profiles. The accuracy of this method is demonstrated also with beam propagation measurements.
1. Introduction The knife-edge method for measuring the spatial profile of a laser beam [ 1,2] has been in use since the invention of the laser itself. Despite the availability of very comfortable camera based beam-profiling systems and the fact, that this method is limited to radially or at least elliptically symmetric beams, it is still used today [3-51. One reason is the high spatial resolution, which is only restricted by the resolution of the mechanical stages (< 1 Km). Especially in micromachining, with focal spots of several 10 pm, beam profile measurements are possible with a simple setup and with high accuracy. The simple and low-cost design makes this method available for most users. In contrast to the pin-hole or camera based methods, when using the knife-edge method, the beam profile is obtained only after differentiating and subsequently transforming the data. The differentiation reduces considerably the signal-to-noise ratio of the 0030418/97/S17.00 PII
calculated profile. A differentiation is not necessary if the data are obtained with the slit method, but slit width smaller than a few p,rn are difficult to produce. The improved method presented here combines the advantages of both the conventional knife-edge method and the slit method. The data are obtained by dithering the slowly moving knife-edge, which makes this method equivalent to the slit method. Using a lock-in amplifier, the modulated part of the beam (the ‘slit’) can be detected. The ‘slit width’ can be varied on a km to sub-km scale by controlling the amplitude of the dither movement. The applicability of this method is demonstrated by measuring the far-field diffraction pattern of a circular aperture at the focus of a lens and comparing it to the theoretical profile. Beam propagation measurements based on the new knife-edge method and on a CCD-camera are also presented. The algorithm that we found most useful for transforming the data, is discussed.
Copyright 0 1997 Elsevier Science B.V. All rights reserved.
SOO30-4018(96)00527-5
W. Pluss er al. / Optics Communicarions
22
2. Transformation
algorithm
The algorithm used for transforming the knifeedge data to a beam profile is related to the geometry depicted in Fig. 1. With a sufficiently small sample spacing a, the intensity at the position rj can be assumed to be a constant Ii within the area Aij and can be calculated from the signals Pi, measured at the positions xi. From Fig. 1, it is clear that each Pi is a weighted sum of Zj, where the weighting factors are given by the areas Aij:
(1) Therefore, the transformation from Pi to Z, is a linear equation: Ij= f &A,,‘P,.
(2)
I
areas Aii and Aij can be calculated by a two-dimensional integration according to
The
Aii
[~a;~6+u’2”“i
=
dy
(3)
dx
I
and
(4) respectively. The transformation given in Eq. (2) obviously does not include any smoothing, which is sometimes
1
F-2 Pl
done with data obtained with the conventional knife-edge method [l]. Note, that the signals of the conventional knifeedge method Pconv,i are related to the signals Pi by ‘i
=
‘c0nv.i
-
‘conv.i-
3. Experimental
Y
t x- moving direction
moving knife edge
Fig. 1. Geometric
illustration
of transformation
algorithm.
(5)
I’
realization
The typical set-up used for knife-edge measurements is shown in Fig. 2. A reference measurement was employed to account for laser power fluctuations. Both, the scan and the reference signals were measured using an integrating sphere to improve the accuracy of this method. A digital lock-in amplifier (Stanford Research Systems SRS 850) detected the modulated signal at the dithering frequency of the knife-edge. The enlarged view in Fig. 2 shows the schematic drawing of the dithering knife-edge. The dither movement of the razor-blade and its lever, which is mounted with a leaf spring, can be achieved by applying a low ac voltage to the piezoelectric transducer. For a sinusoidal voltage, the oscillation of the razor blade is also sinusoidal in scan direction. The oscillation frequency was chosen to be the mechanical resonance frequency (217 Hz) of the lever, because the amplitude was most stable in this case. The oscillation frequency determines the minimum time constant of the lock-in amplifier and subsequently the measurement time, which was about one minute for a resolution of 100 points/scan.
4. Measurements methods
2t Pi
I34 (1997) 21-24
and
comparison
with
other
The advantage of the dithering knife-edge method compared to the conventional knife-edge method is demonstrated in Fig. 3, where the beam profile of an unfocused He-Ne laser beam is shown, as measured using the two methods. The enhanced signal-to-noise ratio of the dithering knife-edge is clearly visible. In fact, the signal-to-noise ratio of the used detectorlock-in-amplifier combination, which is about lo6 : 1, is maintained in the beam profile. The accuracy of this knife-edge method was tested by comparing a measured and calculated profile of a
W. Plass et al./Optics
Beam-splitter
Communications
23
134 (1997) 21-24
Laser
integrating sphere Knite-edge
Razor blade
Piezo-transducer Leaf spring
Fig. 2. Scheme of experimental
set-up.
He-Ne laser beam (diameter 2.5 mm, 0 < 1 mrad) in the far-field of a 0.9 mm aperture. The far-field profile was measured in the focal plane of a lens (f= 30 mm). An excellent correspondence can be observed, see Fig. 4. Scanning such a profile with a pin-hole is a difficult task because the position of the minima depends critically on the positioning of the pin-hole with respect to the center of the laser beam, whereas the measured intensity at the minima is too high if the aperture of the pin-hole is too large. For an investigation and theoretical discussion of laser beam propagation, beam width measurements are often useful and necessary [2,6,7]. Beam width data obtained with the dithering knife-edge method have therefore been compared to data obtained by a low-noise liquid-nitrogen cooled CCD camera (Astromed LNC, S/N-ratio: 3 X 104/1; 16 bit resolution). The measurements were done along the propagation axis of a He-Ne laser beam. Fig. 5 depicts the beam widths, measured with both methods according to the second-moment definition. Both methods agree
Fig. 4. Far-field profile of a He-Ne laser beam, diameter 2.5 mm, aperture diameter 0.9 mm, in the focal plane of a lens, f’= 30 mm, as measured by the dithering tmife-edge method and calculated analytically.
well with each other. Here the low signal-to-noise ratio of the dithering knife edge is especially important, as the second-moment definition of the beam diameter is very sensitive to a noisy signal.
5. Conclusions The dithering knife-edge is a new method for beam profiling with high accuracy and high spatial resolution. The spatial resolution can be extended far below the sub-p.m level. Unlike the conventional knife-edge method, the dithering knife-edge yields the same signal-to-noise ratio for the beam profile that can be realized with the detector-lock-in-amplifier combination. Hence, the transformation algorithm used for obtaining the beam profile from knife-edge data does not need to smooth the data. An
1
0
Fig. 3. Beam profile knife-edge.
measured
with conventional
and dithering
IO
Irn
1m
35.3
C?CQ&LlzWl, oshn2a.g
4w
A50
Fig. 5. Knife-edge and camera based 2nd-moment beam width measurements along the propagation axis. For comparison, the measurements are referenced to each other.
24
W. Pluss et d/Optics
Communications
excellent agreement could be achieved in a comparison of measured and calculated focused-beam profiles. For determining beam diameters, the dithering knife-edge method also agrees well with measurements obtained by a high resolution CCD camera.
Acknowledgements
This work was partly supported by the Bundesministerium fur Forschung und Technologie under Contract 13 N 5809.
134 (1997) 21-24
References [I] R.M. O’Connell and R.A. Vogel, Simple accurate inversion of knife edge data from radially symmetric laser beams, in: Laser Induced Damage in Optical Materials 1985, NBS, Spec. Publ. 746 (1988). [2] D.R. Skinner and R.E. Whitcher, J. Phys E 5 (1972). [3] R.M. Wood, Laser Damage in Optical Materials (Adam Hilger, Bristol-Boston, 1986). [41 A.E. Siegmamr, M.W. Sasnett and T.F. Johnson, IEEE J. Quantum Electron. 27 (4) (1991) 1098. [s] J. Hue, J. Dijon and P. Lyan, in: Laser Induced Damage in Optical Materials 1992, SPIE Vol. 1848 (1993) p. 125. (61 K. Wittig, R. Maestle and A. Giesen, in: Beam Control, Diagnostics, Standards and Propagation, 1995, SPIE Vol. 2375 (1995) p. 306. 171 ISO/DIS I1 146, Test methods for laser beam parameters, beam widths, divergence angle and laser beam propagation factor, ISO, The International Organization for Standardization ( 1995).