Optics: measuring and testing – By polarized light examination – With birefringent element
Patent
1990-04-11
1991-09-17
Turner, Samuel
Optics: measuring and testing
By polarized light examination
With birefringent element
356347, 73657, G01B 902
Patent
active
050489640
DESCRIPTION:
BRIEF SUMMARY
The present invention has been conceived and developed for extracting phase information in electronic speckle pattern interferometry, or so-called ESPI, by the phase-stepping technique and it is convenient to describe the invention in this context. However, it is to be understood that the invention is applicable to other forms of interferometry for which the phase-stepping technique is appropriate.
This technique involves successively changing the phase of one of the interferometer beams from a datum phase .phi. by 2.pi./k in (k-1) equal steps and recording the respective interference pattern images generated at each different phase. The Fourier series coefficients for the datum phase are then given by the expressions ##EQU1## where N is the image number in the phase-stepping sequence and I.sub.N (x,y) is the image pixel intensity. A solution for .phi.(x,y) is then given, in turn, by the expression
However, the technique is not without practical difficulties.
For a given image resolution, image recording and related equipment needs increase with k and so also, in general terms, will the time taken for computation by virtue of the increased number of pieces of data involved in the expressions to be evaluated.
At the same time, the environmental sensitivity of the optical instrumentation can drift and introduce error in I.sub.N as k increases.
In practice these difficulties are such that the technique is usually deployed with k equal to 3 or 4, when evaluation is respectively given by ##EQU2## When k is 3 the expression to be evaluated is computationally more complex than that for k equal to 4, but environmental sensitivity is higher. Higher values of k are relatively impracticable by virtue of greatly increased equipment cost and/or complexity plus poor sensitivity.
Clearly this situation is such that the case when k is 2 appears particularly attractive. However, in this case it will be seen that .beta..sub.1 is zero.
An object of the present invention is to reduce the difficulties of the above situation and to this end there is provided an interferometric method comprising, and related apparatus for, generating two signals representing the point-by-point variations in intensity of respective patterns of electromagnetic radiation resulting from the interference of first and second beams of such radiation derived from a coherent source, with at least the first beam for each pattern being scattered, before interference with its respective second beam, from a common object surface, and with a corresponding pair of the beams, one for each pattern, having a predetermined relative phase difference of other than a multiple of .pi.; and determining from said two signals values for a datum phase of the radiation at said surface.
The derivation of the invention can be explained by considering, for ESPI, the case for k equal to 3 to produce images at phases .phi.-.delta., .phi. and .phi.+.delta.. These images can be expressed in a simplified manner by the equations ##EQU3## Included in these equations are DC components I.sub.O plus I.sub.R contributed by the object and reference beams producing the images. Elimination of these components, such as by selective frequency filtering or substraction, allows further simplification effectively to represent a situation where k is 2 by forming from only two of the equations an expression for .phi..
Thus from equations (1) and (2), .phi. is given by ##EQU4## and if .delta. is chosen for convenience as .pi./2 or an odd multiple thereof, this expression is further simplified to
From equations (1) and (3), .phi. is given by ##EQU5## and if .delta. is chosen for convenience as .pi./4, or an odd multiple thereof, cot .delta. equals .+-.1.
For further clarification the accompanying drawing schematically illustrates, by way of example, one embodiment of electronic speckle pattern interferometric apparatus according to the invention.
The illustrated apparatus comprises a coherent light source, laser 1, which projects a beam by way of a beam splitter 2 to an object surface 3 of interest
REFERENCES:
patent: 3694088 (1972-09-01), Gallagher et al.
patent: 3772457 (1973-11-01), Macovski
patent: 3828126 (1974-08-01), Ramsey
patent: 4583855 (1986-04-01), Bareket
Applied Optics, vol. 26, No. 6, 15 Mar. 1987 (New York, N.Y., US), C. Ai et al: "Effect of Piezoelectric Transducer Nonlinearity on Phase Shift Interferometry", pp. 1112-1116.
Tyrer et al., "Use of High Resolution Real-Time Image Processing Techniques in Generation and Analysis of ESPI Fringe Patterns", Opt. Lasers Eng. (UK), vol. 8, No. 1988, pp. 109-121.
Tyrer et al., "The Application of Phase Stepping to the Analysis of ESPI Fringe Patterns", Proc. SPIE Int Soc. Eng., vol. 814, part 1, 1988, pp. 379-389.
Kerr David
Mendoza-Santoyo Fernando
Tyrer John R.
National Research Development Corporation
Turner Samuel
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