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Measurement of spatial coherence using modified Michelson stellar interferometer
MEASUREMENT OF SPATIAL COHERENCE USING MODIFIED MICHELSON STELLAR INTERFEROMETER T. ASAKURA & H. FUJIWARA Applied Physics Department, Hokkaido University, Japan
A modification of the Michelson stellar type of interferometer is described which allows quantitative measurement of the spatial coherence of light beams from various kinds of source. This method is especially useful for the measurements of the degree of spatial coherence of laser beams and has been experimentally employed to explore the spatial coherence of laser beams operating in a degenerate TEM o1 mode.
COHERENCE properties of light beams have long been studied by many workers. Much attention has been devoted to the theoretical work of optical coherence theory. But it seems that much less progress has been made with the actually measuring the coherence properties of light, although the subject is of increasing importance in a number of problems of practical interest. . It is known that partial coherence plays an important
role in a microscope 1 or spectroscope 2 and the intensity interferometer of Hanbury Brown & Twiss 3 , developed for the measurement of stellar diameters. The study of the coherence properties of a laser beam is specially important since the laser is being increasingly used as a light source not only in existing optical instruments but also in various new instruments for optical information processing. The coherence properties of lasers are still not fully investigated although some studies 4 have been conducted on various aspects of coherence for two types of ruby and gas lasers. This paper describes a new method for measuring the spatial coherence of light beams, developed specially for investigating the spatial coherence of laser beams. This method is then used to the measurement of spatial coherence of a He-Ne laser light. MODIFIED MICHELSON STELLAR INTERFEROMETER
Coherence properties of light beams can usually be studied in association with interference phenomena since these phenomena may be considered as manifestation of two-point correlation in a light beam. The majority of methods used for quantitatively measuring the spatial coherence between two points in a light beam are based on Young's interference experiment. Among them, a method extensively used is the one developed by Thompson & Wolf 5 who conducted Young's experiment by using the diffractometer. In their experiment the degree of spatial coherence is obtained by inspection of the visibility of fringes pro-
duced on the Fraunhofer diffraction plane by two light beams emergent from two circular apertures with variable separation. This method has two shortcomings. One is that a lot of masks consisting of two small identical circular apertures with various separations have to be prepared to determine the degree of spatial coherence over a large area. The other is that it is usually quite difficult to obtain faithful record of the very fine fringes produced by increasing the separation of the apertures on a photographic plate or photoelectric detector. The visibility of these fine fringes cannot be recorded by a photographic method because of the nonlinearity of the H-D curve and of the modulation transfer properties of the photographic plate. In place of the photographic plate a photomultiplier with a very narrow slit in front can be used for quantitative measurements on the fringes, but there is obviously a limitation on preparation of this narrow slit, making measurement of spatial coherence over a large area impossible. To avoid these defects inherent in the usual Youngtype experiment, we modify the well-known method of Michelson for measuring the angular diameter of stars. This method is in fact a device for measuring the degree of coherence based on Young's experiment. !n Michelson's method varying the distance of two mirror s which receive light from the star is equivalent to changing the separation of two circular apertures in Young's experiment. This operation on two mirrors does not change the fringe interval, determined by the separation distance of two holes placed in front of the Fourier transforming lens. By varying the distance of mirrors and observing various fringes of equal fineness but of different visibilities, the degree of coherence is finally measured. Thus we see that Michelson's stellar interferometer has solved two defects in Young's experiment. As a modification of Michelson's method for measurement of the degree of spatial coherence in the laboratory,
Optics Technology May 1969
157
a new method is proposed here and is shown in Fig.!. The light from a laser source La is concentrated by a microscope objective Mc on a point Q which becomes a secondary source. By placing the proper pinhole at Q or moving the ground-glass screen, the secondary source is controllable. Light from the point Q is made parallel by lens L 1 . The parallel light is reflected by a movable prism P l ' two fixed mirrors Ml' M 2 and a fixed prism P 2 , and it then traverses the two small identical circular apertures on a black screen S placed in front of a objective lens L 2 · The prisms P 1 and P 2 , whose two surfaces facing the incoming light are coated with silver, act as reflecting mirrors. Young's interference fringes are observed in the focal plane F of the objective. The separation of the two apertures at S is fixed to produce fringes whose intervals are equal and easily adjusted to take a record on the photographic plate or by the photomultiplier. Along the optic axis the large prism P 1 is precisely movable with a micrometer screw which automatically varies the separation distance, 2a, of light beams traversing the two apertures. The distance 2a plays a fundamental role in the present method. The degree of coherence for light at the two points of separation 2a and illuminated by parallel light is measured by observing fringes produced on the plane F. By moving the prism P 1 along the optic axis we vary the degree of coherence and then explore the spatial coherence over the light beam. Special care was taken to read the distance moved of the prism P 1 and to equalize the two optical path lengths from the prism P 1 to the two apertures on S with the mirrors M1' M 2 and the prism P 2 . Equality of these path lengths is very important for light from a thermal source because of its time coherence being relatively short, but less important for the laser light whose time coherence is relatively long. The central part of Fig. 1 is shown in Fig.2. SPATIAL COHERENCE OF HE -NE LASER BEAM In the present experiment, measurements have been made by the new method of Fig. 1 on the spatial coherence of a He-Ne laser with a cavity of the external concave mirror type. The mode examined is a degenerate TEM o1 (a composition of TEM oo and TEM 10 ) shown in Fig. 3. The interference fringes at
Fig. 2. Photograph of an actual arrangement for the central part of Fig. 1.
Fig. 3. Degenerate TEM o1 mode exammed by using the interferometer o/Fig. 1. the plane F are recorded on the photographic plate, if the patterns are to be stored in the pictures, or scanned by the photomultiplier if quantitative examination of the patterns is desirable. Spatial coherence of the present laser mode has been explored by moving equally the two points Pl and P2 from the centre 0 to the outside along the line indicated in Fig. 3. Records obtained with the method
s F
Fig. 1. Block diagram of modified Michelson-type interferometer for measuring the spatial coherence of light beams. 158
Optics Technology May 1969
2a=2·3mm
2a=8·1mm
2a=9·2mm
2a=10·4mm
Fig. 4. Record of interference fringes as a function of separation distance 2a of the two points. Curves corresponding to the cause indicated by the full line of Fig. 5. Fraunhofer diffraction patterns 7 , the Mach-Zehnder interferometerS, the polarization interferometer 9 and the optical fibers 10 have been used. Compared with these methods, the present method is very simple and especially useful for exploring the spatial coherence of laser beams. This interferometer has actually been employed to investigate the spatial coherence of laser beams operating in a degenerate TEM o1 mode and its usefulness is verified experimentally.
1-0 iii
gO-8 CII
L.
CII
-50·6 u
~0·4 ~
01
~0-2
4
8 12 16 20 24 26 32 36 2a separation distance over magnified laser beams [mm]
40
Fig.S. Degree of spatial coherence IY1ZI for the degenerate TEM o1 modes obtained at variolAs distances, 2a, between two points on crosssection of magnified laser beams under three slightly different conditions. (Magnification of original laser beam is x14.) Measured data are indicated by dotted points. described are shown in Fig. 4 with various separations of the two points over the mode. The curves in Fig.4 show the visibility of the fringes for various separations in the mode pattern. The degree of coherence IY1ZI calculated from the visibility is shown in Fig. 5 for three slightly different conditions. The laser was used on three days and the mirrors of the cavity moved very slightly without changing the outline of the mode pattern. The intensities of light passing the two apertures on S have been checked to have almost equal values. The parallel light passing the lens L 1 is a magnified cross-section of the laser mode under oscillation, so that we can easily study the coherence properties for different points of the mode. Mor ley et al 6 have inve stigated the spatial coherence when a combination of TEM oo and TEM 10 (a degenerate TEM o1 mode is in oscillation and have obtained good agreement between theoretical and experimental data. Our results in Fig. 5 for the degree of spatial coherence of three degenerate TEM o1 modes is in fairly good agreement with the work of Morley et al.
ACKNOWLEDGMENT The authors wish to express their thanks to Ohara Optical Glass Manufacturing Company for the supply of prisms used in the interferometer. They are very much indebted to Mr. H. Fujii for contributions in the experimental work and to Professor K. Murata for his interest in this investigation. REFERENCES 1
Hopkins, H. H. & Barham, P. M. Proc. Phys. Soc. vol. 63. 1950. p. 737.
2
Wolf, E. Japan J. Appl. Phys. vol. 4, Suppl.l. 1965. p.l.
3
Hanbury Brown, R. &Twiss, R. Q. Nature, vol. 177. 1956. p.27 and vol. 178. 1956. p.1046.
4
Berkley, D. A. & Wolga, G. J. Phys. Rev. Lett. vol. 2. 1962. p.479. Herriott, D. R. J. Opt. Soc. Am. vol. 52. 1962. p.3l. Bertolotti, M., Daino, B. &Sette, D. Nuovo Cimento, vol. 33. 1964. p.1705. Bertolotti, M., Daino, B., Gori. F. &Sette, D. Nuovo Cimento, vol. 38. 1965. p.1505.
5
Thompson,B.J.&Wolf,E. J.Opt.Soc.Am.vol.47. 1957. p.895.
6
Morley, D. C. W., Schofield, D. G., Allen, L. & Jones, D. G. C. Brit. J. Appl. Phys. vol. 18. 1967. p.1419.
7
Cornacchio,J. V. & Farnham,K. A. Nuovo Cimento, vol. 42. 1966. p.108.
8
JanossY,M.,Csillag,L.&Kantor,K. Phys.Lett. vol. 18. 1965. p.124. Janossy, M., Csillag, L. &Kantor, K. Phys. Lett. vol. 20. 1966. p.636.
9
Fran~on, M. &Mallick, S. Progress in Optics, vol. 6. 1967. p.73. (edited by E.Wolf).
10
Suzuki, T. Japan J. Appl. Phys. vol. 6. 1967. p.343.
CONCLUSION We have shown a new method for measuring the spatial coherence of light beams in the laboratory using a modified Michelson -type interferometer. In addition to the methods described earlier other methods have been employed by several workers.
Optics Technology May 1969
159
A modification of the Michelson stellar type of interferometer is described which allows quantitative measurement of the spatial coherence of light beams from various kinds of source. This method is especially useful for the measurements of the degree of spatial coherence of laser beams and has been experimentally employed to explore the spatial coherence of laser beams operating in a degenerate TEM o1 mode.
COHERENCE properties of light beams have long been studied by many workers. Much attention has been devoted to the theoretical work of optical coherence theory. But it seems that much less progress has been made with the actually measuring the coherence properties of light, although the subject is of increasing importance in a number of problems of practical interest. . It is known that partial coherence plays an important
role in a microscope 1 or spectroscope 2 and the intensity interferometer of Hanbury Brown & Twiss 3 , developed for the measurement of stellar diameters. The study of the coherence properties of a laser beam is specially important since the laser is being increasingly used as a light source not only in existing optical instruments but also in various new instruments for optical information processing. The coherence properties of lasers are still not fully investigated although some studies 4 have been conducted on various aspects of coherence for two types of ruby and gas lasers. This paper describes a new method for measuring the spatial coherence of light beams, developed specially for investigating the spatial coherence of laser beams. This method is then used to the measurement of spatial coherence of a He-Ne laser light. MODIFIED MICHELSON STELLAR INTERFEROMETER
Coherence properties of light beams can usually be studied in association with interference phenomena since these phenomena may be considered as manifestation of two-point correlation in a light beam. The majority of methods used for quantitatively measuring the spatial coherence between two points in a light beam are based on Young's interference experiment. Among them, a method extensively used is the one developed by Thompson & Wolf 5 who conducted Young's experiment by using the diffractometer. In their experiment the degree of spatial coherence is obtained by inspection of the visibility of fringes pro-
duced on the Fraunhofer diffraction plane by two light beams emergent from two circular apertures with variable separation. This method has two shortcomings. One is that a lot of masks consisting of two small identical circular apertures with various separations have to be prepared to determine the degree of spatial coherence over a large area. The other is that it is usually quite difficult to obtain faithful record of the very fine fringes produced by increasing the separation of the apertures on a photographic plate or photoelectric detector. The visibility of these fine fringes cannot be recorded by a photographic method because of the nonlinearity of the H-D curve and of the modulation transfer properties of the photographic plate. In place of the photographic plate a photomultiplier with a very narrow slit in front can be used for quantitative measurements on the fringes, but there is obviously a limitation on preparation of this narrow slit, making measurement of spatial coherence over a large area impossible. To avoid these defects inherent in the usual Youngtype experiment, we modify the well-known method of Michelson for measuring the angular diameter of stars. This method is in fact a device for measuring the degree of coherence based on Young's experiment. !n Michelson's method varying the distance of two mirror s which receive light from the star is equivalent to changing the separation of two circular apertures in Young's experiment. This operation on two mirrors does not change the fringe interval, determined by the separation distance of two holes placed in front of the Fourier transforming lens. By varying the distance of mirrors and observing various fringes of equal fineness but of different visibilities, the degree of coherence is finally measured. Thus we see that Michelson's stellar interferometer has solved two defects in Young's experiment. As a modification of Michelson's method for measurement of the degree of spatial coherence in the laboratory,
Optics Technology May 1969
157
a new method is proposed here and is shown in Fig.!. The light from a laser source La is concentrated by a microscope objective Mc on a point Q which becomes a secondary source. By placing the proper pinhole at Q or moving the ground-glass screen, the secondary source is controllable. Light from the point Q is made parallel by lens L 1 . The parallel light is reflected by a movable prism P l ' two fixed mirrors Ml' M 2 and a fixed prism P 2 , and it then traverses the two small identical circular apertures on a black screen S placed in front of a objective lens L 2 · The prisms P 1 and P 2 , whose two surfaces facing the incoming light are coated with silver, act as reflecting mirrors. Young's interference fringes are observed in the focal plane F of the objective. The separation of the two apertures at S is fixed to produce fringes whose intervals are equal and easily adjusted to take a record on the photographic plate or by the photomultiplier. Along the optic axis the large prism P 1 is precisely movable with a micrometer screw which automatically varies the separation distance, 2a, of light beams traversing the two apertures. The distance 2a plays a fundamental role in the present method. The degree of coherence for light at the two points of separation 2a and illuminated by parallel light is measured by observing fringes produced on the plane F. By moving the prism P 1 along the optic axis we vary the degree of coherence and then explore the spatial coherence over the light beam. Special care was taken to read the distance moved of the prism P 1 and to equalize the two optical path lengths from the prism P 1 to the two apertures on S with the mirrors M1' M 2 and the prism P 2 . Equality of these path lengths is very important for light from a thermal source because of its time coherence being relatively short, but less important for the laser light whose time coherence is relatively long. The central part of Fig. 1 is shown in Fig.2. SPATIAL COHERENCE OF HE -NE LASER BEAM In the present experiment, measurements have been made by the new method of Fig. 1 on the spatial coherence of a He-Ne laser with a cavity of the external concave mirror type. The mode examined is a degenerate TEM o1 (a composition of TEM oo and TEM 10 ) shown in Fig. 3. The interference fringes at
Fig. 2. Photograph of an actual arrangement for the central part of Fig. 1.
Fig. 3. Degenerate TEM o1 mode exammed by using the interferometer o/Fig. 1. the plane F are recorded on the photographic plate, if the patterns are to be stored in the pictures, or scanned by the photomultiplier if quantitative examination of the patterns is desirable. Spatial coherence of the present laser mode has been explored by moving equally the two points Pl and P2 from the centre 0 to the outside along the line indicated in Fig. 3. Records obtained with the method
s F
Fig. 1. Block diagram of modified Michelson-type interferometer for measuring the spatial coherence of light beams. 158
Optics Technology May 1969
2a=2·3mm
2a=8·1mm
2a=9·2mm
2a=10·4mm
Fig. 4. Record of interference fringes as a function of separation distance 2a of the two points. Curves corresponding to the cause indicated by the full line of Fig. 5. Fraunhofer diffraction patterns 7 , the Mach-Zehnder interferometerS, the polarization interferometer 9 and the optical fibers 10 have been used. Compared with these methods, the present method is very simple and especially useful for exploring the spatial coherence of laser beams. This interferometer has actually been employed to investigate the spatial coherence of laser beams operating in a degenerate TEM o1 mode and its usefulness is verified experimentally.
1-0 iii
gO-8 CII
L.
CII
-50·6 u
~0·4 ~
01
~0-2
4
8 12 16 20 24 26 32 36 2a separation distance over magnified laser beams [mm]
40
Fig.S. Degree of spatial coherence IY1ZI for the degenerate TEM o1 modes obtained at variolAs distances, 2a, between two points on crosssection of magnified laser beams under three slightly different conditions. (Magnification of original laser beam is x14.) Measured data are indicated by dotted points. described are shown in Fig. 4 with various separations of the two points over the mode. The curves in Fig.4 show the visibility of the fringes for various separations in the mode pattern. The degree of coherence IY1ZI calculated from the visibility is shown in Fig. 5 for three slightly different conditions. The laser was used on three days and the mirrors of the cavity moved very slightly without changing the outline of the mode pattern. The intensities of light passing the two apertures on S have been checked to have almost equal values. The parallel light passing the lens L 1 is a magnified cross-section of the laser mode under oscillation, so that we can easily study the coherence properties for different points of the mode. Mor ley et al 6 have inve stigated the spatial coherence when a combination of TEM oo and TEM 10 (a degenerate TEM o1 mode is in oscillation and have obtained good agreement between theoretical and experimental data. Our results in Fig. 5 for the degree of spatial coherence of three degenerate TEM o1 modes is in fairly good agreement with the work of Morley et al.
ACKNOWLEDGMENT The authors wish to express their thanks to Ohara Optical Glass Manufacturing Company for the supply of prisms used in the interferometer. They are very much indebted to Mr. H. Fujii for contributions in the experimental work and to Professor K. Murata for his interest in this investigation. REFERENCES 1
Hopkins, H. H. & Barham, P. M. Proc. Phys. Soc. vol. 63. 1950. p. 737.
2
Wolf, E. Japan J. Appl. Phys. vol. 4, Suppl.l. 1965. p.l.
3
Hanbury Brown, R. &Twiss, R. Q. Nature, vol. 177. 1956. p.27 and vol. 178. 1956. p.1046.
4
Berkley, D. A. & Wolga, G. J. Phys. Rev. Lett. vol. 2. 1962. p.479. Herriott, D. R. J. Opt. Soc. Am. vol. 52. 1962. p.3l. Bertolotti, M., Daino, B. &Sette, D. Nuovo Cimento, vol. 33. 1964. p.1705. Bertolotti, M., Daino, B., Gori. F. &Sette, D. Nuovo Cimento, vol. 38. 1965. p.1505.
5
Thompson,B.J.&Wolf,E. J.Opt.Soc.Am.vol.47. 1957. p.895.
6
Morley, D. C. W., Schofield, D. G., Allen, L. & Jones, D. G. C. Brit. J. Appl. Phys. vol. 18. 1967. p.1419.
7
Cornacchio,J. V. & Farnham,K. A. Nuovo Cimento, vol. 42. 1966. p.108.
8
JanossY,M.,Csillag,L.&Kantor,K. Phys.Lett. vol. 18. 1965. p.124. Janossy, M., Csillag, L. &Kantor, K. Phys. Lett. vol. 20. 1966. p.636.
9
Fran~on, M. &Mallick, S. Progress in Optics, vol. 6. 1967. p.73. (edited by E.Wolf).
10
Suzuki, T. Japan J. Appl. Phys. vol. 6. 1967. p.343.
CONCLUSION We have shown a new method for measuring the spatial coherence of light beams in the laboratory using a modified Michelson -type interferometer. In addition to the methods described earlier other methods have been employed by several workers.
Optics Technology May 1969
159