Abstract

We describe a double-grating interferometer that has a one-to-one correspondence with a Michelson interferometer. The half spatial periods of the gratings are equivalent to the wavelengths of the interferometer. The widths of the interference fringes can be changed easily. The intensity distribution of the interference pattern is independent of the wavelength of the light source used. The surface profile of an object can be measured because two interference beams can coincide precisely on the image plane of the object. The measuring range is much larger than that of a Michelson interferometer.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, 1999), pp. 313–352.
  2. O. Sasaki and H. Okazaki, Appl. Opt. 25, 3137 (1986).
    [CrossRef]
  3. O. Sasaki and H. Okazaki, Appl. Opt. 24, 2124 (1985).
    [CrossRef]
  4. O. Sasaki and H. Okazaki, Appl. Opt. 25, 3152 (1986).
    [CrossRef]

1999 (1)

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, 1999), pp. 313–352.

1986 (2)

1985 (1)

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Basic schematic of a double-grating interferometer: (a) ±1st-order beams precisely superposed upon the image plane of grating G1, (b) +1+1st and -1-1st order beams precisely superposed upon the image plane of grating G2.

Fig. 2
Fig. 2

Interference patterns for six values of β1.

Fig. 3
Fig. 3

Equivalent wavelength d1/2 is independent of β1.

Fig. 4
Fig. 4

Experimental double-grating interferometer for surface profile measurement: LD, laser diode.

Fig. 5
Fig. 5

Interference fringe patterns of the surface of a plane mirror and a stainless-steel sheet: M, plane mirror; O, stainless-steel sheet.

Fig. 6
Fig. 6

Surface profiles of the plane mirror and the stainless-steel sheet.

Fig. 7
Fig. 7

Real surface profiles of the object: (a) Fig. 6(b) minus Fig. 6(a); (b) Fig. 6(d) minus Fig. 6(c).

Fig. 8
Fig. 8

Figure 7(a) minus Fig. 7(b).

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

Gix=ngin expi2πnx/di cos βi,
Ix=2B21+cos2πx/T,
T=2m2m1/d1 cos β1-1/d2-1.
Ix,l1,l2=2B21+cos2πx/T+4πl1/d1-4πl2/d2.
Ix,l1,t=2B21+cosZ cosωct+θ+α,
α=2πx/T+4πl1/d1,
α=2πx/T+4πl1/d1+42πr/d1,

Metrics