NASA TECHNICAL TRANSLATION NASA TT F-14,008
A METHOD OF STUDYING VERY WEAK PHASE OBJECTS
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'
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
WASHINGTON, D. C. 20546 OCTOBER 1971
A METHOD OF STUDYING VERY WEAK PHASE OBJECTS
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 (O.ly 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-  .
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
Ty^lT^^y (.AA'.O : 
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:
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  . 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.
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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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 .
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.
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,
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
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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