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[ill- SS'O'ff 


Henri Royer and Felix Albe 


Translation of "Une m^thode d 'etude des 

tr&s faibles objets' de phase", Comptes 

Rendu, Academie des Sciences, Paris, „ 

Vol. 270, February 23, 1970, pp. 525-528 ilf' 






Henri Royer and Felix Albe 

ABSTRACT. A phase object is illuminated by means of a 
laser. It is analyzed by means of a half -wave lamina which 
is defocalized with respect to its Fourier plane. One or 
several fringes are observed in the image. Their deforma- 
tions give an exact measure of phase gradients in the object. 

The usual detection methods for very weak phase objects can be cate- /525 
gorized into two categories: 

— Interferential methods which result in a map of optical paths in the 
object in the form of a fringe distribution which is alternately dark and light. 
The deformations of these fringes are directly connected with the variations 
in the optical path within the object. Their importance can be determined by 
a geometrical measurement. 

— Strioscopic methods which show the gradients of the optical path. 


A photometric measurement is required in order to evaluate these gradients 
which are connected with the variations of illui 
accuracy of this measurement remains uncertain. 


which are connected with the variations of illumination in the image . The 


Numbers in the margin indicate pagination in the original foreign text. 

Note: Presented by M. Alfred Kastler . Session of February 2, 1970 


Differential interferometry is presently being used at the I.S.L. It 

cannot be assimilated into a strioscopic method unless the shift between the 
two interfering waves is small with respect to the details being observed. 
Its sensitivity, therefore, becomes too small so that it cannot be applied to 
,very weak objects of interest here. 

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The smallest defect which can be detected by an interferometer (dif- 
ferential or nondifferential) is limited, in any case, by the wave nature of 
the light ( for a two-wave interferometer). The sensitivity of a strio- 
scopic current can be increased indefinitely, at least according to theory. 
The method proposed intends to combine the advantages of the two above methods. 
These are: increased sensitivity and adjustability as a function of the object, 
as well as accuracy and ease of carrying out geometric measurements. 

Strioscopv by Amplitude Subtraction 

A classical strioscopic configuration with coherent light is used in 
which a half-plane which dephases by 180° is substituted for the analysis 
knife edge. The negative frequencies of the object are subtracted from the 
positive frequencies in _^this way, and an image is observed in which the dark 
regions correspond to points of the object where the optical path gradients 
are zero [1-3] . 

Introduction of an Imperfection 
in the Calibration 

A defocalization of the lamina filter is equivalent to a quadratic phase 
imperfection in the object. A black fringe intersects the field parallel to 
the half plane edge. The dimension t of this fringe decreases in proportion 
to the increase in the defocalization e: 

/fla -J- [5] . 

The presence of a weak gradient in the optical path A introduces a 
deformation of the fringe at the points corresponding to the object. If R 
designates the distance from the filter to the object and 6y is the deformation 
of the fringe along the y axis referred to the object space, then we have 

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In this way it is seen how by a voluntary introduction of a calibration 
imperfection makes it possible to dispense with the densitometer. The sensi- 
tivity a of the configuration, the ratio of the phase difference to the 
gradient causing it, can be adapted quite flexibly to the size of the imper- 
fection being measured: 


Figure 1. 

Just as in interferential systems, the accuracy is always limited by the 
size of the black fringe [3, 4]. 




Positioning of a More Elaborate Filter 

This method can be criticized because precise indications only result for 
points located along the one fringe. In order to increase the amount of in- 
formation regarding the object, it appears desirable to multiply the number 
of fringes in the iftage field. This leads to the idea of replacing the half- 
plane filter by a periodic grid of dephasing bands (Figure 2) . 

It has been shown thatj if the step p of the grid is sufficiently large, 
a series of rectilinear and parallel fringes are formed in the image [5] . The 
interfringe i, referred to the plane object, is proportional to the period p 
of the grid: 

. J_ /; U pT 

p must therefore be selected so that 1 remains larger than the fringe size 
for a given sensitivity. 








Figure 2. 


Figure 3. 

It seems to be a delicate, if not an impossible, matter to build such a 
filter in a correct manner. In effect, the battlement function can be re- 
placed by a staircase where each step has a "height" equal to it. Such a 
staircase corresponds to a superposition of half-planes which dephase by tt 

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Figure 4. 

Figure 5. 

and shift successively by p/2. It is relatively easy to make, and the 
result is the same (Figure 3) from the point of view of interferences [5]. 


6 —1 
In the present experiments, we used a sensitivity of cf = 2.10 mm.rd . 

Thus, it was possible to measure gradients in the optical path on the order 
of a second of arc. With this sensitivity, this method of course becomes very 
well suited for the calibration of very small phase imperfections (for ex- 
ample, low pressure aerodynamic phenomena). For more pronounced imperfections, 
a very high degree of accuracy can be achieved. This can be used for correc- 
tion of optical system aberrations and for studies in fluids at normal pressure. 

As an example. Figures 4 and 5 show part of the influence of a wake of a 
hypersonic projectile (v = 3400 m/s, p = 60 mm of mercury) on the obtained 
fringes. These are also indicated by the effluence from a candle flame. 

(French-German Institute 
of Research at Saint Louis, 
68-Saint-Louis , Haut-Rhin. ) 


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1. Royer, H. Simultaneous Use of Images Transmitted and Reflected by a 

Foucault Knife (Technical Note I.S.L., T30/66) . 

2. Lowenthal, S. and Y. Belvaux. Appl. Phys. Lett., Vol. 11, No. 2, 1967, 

p. 49. 

3. Royer, H. Strioscopy by Amplitude Substraction (Technical Note I.S.L., 

T. 36/69) . 

4. Oudin, L. and P. Smigielski. Strioscopy by Amplitude Subtraction. 

Mathematical Study (Technical Note I.S.L., T. 41/69). 

5. Albe, F. Method of the Study of Phase Objects by Optical Filtration 

Using a Grid which Introduces a Periodic Dephasing of ir. Application to 
Wakes of Spheres in Hypersonic Flight at Low Pressures (Technical Note 
I.S.L., T.1/70). 

6. Knobs, S. A Quantitative Schlieren Technique for Measuring One-Dimension- 

al Density Gradients in Transparent Media (Proc. 8th Congress on High- 
Speed Photography, Stockholm j June 1968). 

Translated for National Aeronautics and Space Administration under Contract 
NASw 2035 by SCITRAN, P. 0. Box 5456, Santa Barbara, California 93108. 


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