Method for direct phase measurement of radiation, particularly light radiation, and apparatus for performing the method

A method for direct phase measurement of radiation, more particularly light radiation, which is reflected by a body or object with a diffusely reflecting surface. In order to make possible measurement of the phase with the production of a single image, the object or body is irradiated with coherent radiation having a predetermined frequency. The reflected radiation is used to produce an image in an image plane using an image forming optical system, a sensor with a plurality of preferably regularly arranged sensor elements being located in the plane. There is a superimposition of reference radiation on the sensor with the same frequency and with a defined phase relationship. In the case of directed object rays coming from a mirror-like body or object, the reference beam is set so that one period of the interference field produced on the sensor by the superimposition of the object and reference beams covers at least three sensor elements. The image forming optical system is designed and set so that the images of the speckles produced by the radiation on the object or body cover at least three sensor elements in the image plane. The phase of the radiation from the object or body is determined on the basis of the intensity signals of the at least three sensor elements.

This invention relates to a method for the direct phase measurement of 
radiation, particularly light radiation, which is reflected from a body 
with a diffusely reflecting surface. Furthermore, the invention relates to 
an apparatus for performing such a method. 
BACKGROUND OF THE INVENTION 
Direct phase measurement may be used as a method for quantitatively 
evaluating line images produced in interferometric methods, or on 
projection of line patterns on objectives, or in moire methods. These 
methods serve to measure the optical path, or measuring the changes in the 
optical path caused by shifting or deformation of light dispersing 
objects, or changes in the refractive index of transparent objects. 
Projection or moire methods serve inter alia for ascertaining 
three-dimensional forms of objects, or the change thereof. 
There has already been a proposal to evaluate line images on the surface of 
a three-dimensional body using phase shift technology. Such a method is 
described in the German Patent Publication 3,723,555 A, but limited, 
however, to projection and moire methods. The content of this prior 
publication is referred to expressly herein. In the known method, at least 
three phase-shifted images are supplied to a computer for evaluation. In 
order to ensure complete and automatic ascertainment of the 
three-dimensional configuration of the surface of the body, that is to say 
in order to ascertain all three-dimensional coordinates for each point of 
the surface of the body, it is mandatory to input at least three 
phase-shifted images to the computer and to evaluate the same, since there 
are three unknowns in the equation for the measured intensity of each 
image point: 
EQU I=a(X)(1+m(x) cos .phi.) 
wherein: 
I=intensity (measured), 
a=background brightness, 
m=contrast and 
.phi.=phase shift (quantity being sought). 
Since it is only the intensity which may be measured, the above-noted 
equation will be seen, as previously mentioned above, to contain three 
unknowns. In order to ascertain the phase shift being sought, it is thus 
necessary to have three equations, this being accomplished by producing 
three phase-shifted images. Details are described in the above-mentioned 
German Patent Application Publication 3,723,555 A, the content of which is 
expressly referred to herein, as previously mentioned. 
In the prior art method, it is possible for the three-dimensional surface 
of a body to be computed even with only one single shot or picture 
thereof, if the additional further information is input to the computer. 
In practice, however, it is frequently desirable, or sometimes even 
mandatory, to ascertain the three dimensional form of the surface of a 
body automatically without the necessity for inputting additional 
information. In such a case, when using the known method, three shots or 
pictures have to be produced. During the time elapsing between the 
production of these shots or pictures, the surface of the body may undergo 
modification. This may consequently lead to excessively inaccurate or even 
useless results. Even more particularly, in the case of vibration 
analysis, the form of the surface must be able to be ascertained by 
producing a single shot or picture. 
It is an object of this invention to provide a method for the direct phase 
measurement of radiation and an apparatus for performing such a method and 
with which method and apparatus complete phase measurement is possible 
with a single shot or picture. 
STATEMENT OF THE INVENTION 
In accordance with the method of the invention for direct phase measurement 
of radiation, a body or object is irradiated with coherent radiation, for 
instance, laser radiation, at a predetermined frequency. Diffusely 
reflected radiation from the body or object is then formed into an image 
in an image forming optical system in an image plane and in which a sensor 
having a multiplicity of preferably regularly arranged sensor elements is 
located. In the case where an analog sensor, for instance, a picture tube 
camera, is used, the sensor element will correspond to the resolution. 
Reference radiation of the same frequency and of a defined phase 
relationship is also projected onto the sensor so that an interference 
field is produced thereon. The reference radiation is set in this respect 
so that one period of the interference field covers at least three sensor 
elements. The image forming optical system is designed and set so that the 
images of the speckles produced by the radiation on the body in the image 
plane cover at least three sensor elements. From the intensity signals of 
the at least three sensor elements, the phase of the radiation on the body 
may be ascertained. 
In the case of irradiation of a diffusely reflecting body or objection, or 
a diffusely dispersing body or object, for instance, a translucent screen, 
with coherent radiation, such as, for instance, laser light, so-called 
speckles will become visible. The physical mechanism of the formation of 
such speckles is known. 
The average diameter of a speckle may be calculated from the formula (see 
Charles Vest: Holographic Interferometry, page 35, published by John Wiley 
& Sons, New York): 
EQU d=1.5 L-z/D 
wherein 
d=mean speckle diameter, 
L=wave length of the radiation, 
z=image distance (distance of the main plane of the image forming optical 
system from the image plane), and 
D=diameter of the image forming optical system (or of the objective from 
the image forming optical system). 
The images of the speckles in the image plane are combined or modulated 
with a preset carrier frequency. The reference radiation has a defined 
phase relationship. Due to the superimposition by way of modulation of the 
reference radiation with the radiation reflected from the body, an 
interference pattern is produced. This interference pattern, which 
corresponds to the carrier frequency, is set so that one period covers at 
least three sensor elements representing pixels. The interference pattern 
produced for each speckle is received by at least three sensor elements 
(pixel=picture element). Therefore, for each speckle at least three 
support points are obtained for ascertaining the phase relationship. For 
one group for three sensor elements, it is thus possible to unambiguously 
ascertain the phase relationship. As a final result in this method of 
procedure, the resolving power of the sensor is reduced to one third, 
since for ascertaining the phase of a point three sensor elements are 
required. This leads to a distinct advantage in that the phase 
relationship may be unambiguously ascertained and computed on the basis of 
one single shot or picture. From the phase relationship, it is then 
possible to find the coordinates of the surface of the body or object, 
using, for instance, the method described in the above-mentioned German 
Patent Publication 3,723,555 A. 
Where directed radiation is employed, as occurs in the case of 
mirror-reflecting to transparent body or object, no speckles occur. The 
interference field on the sensor between the radiation coming from the 
body or object and the reference radiation is then set so that one period 
of the interference field covers at least three sensor elements. 
The method in accordance with the invention is particularly well adapted 
for vibration analysis, that is, analysis of dynamic deformation, for 
non-destructive material testing, for testing contours, such as, for 
instance, contours of teeth, for measurement of deformation, that is 
analysis of static deformation, for interferometric and projective 
methods, for moire methods and for photoelastic methods. 
The sensor elements, corresponding to pixels, may be arranged linearly 
along parallel lines with preferably equal spacing. Preferably, the image 
forming optical system is designed and, respectively, adjusted so that the 
images of the speckles produced by the radiation on the body or object in 
the image plane cover at least three adjacently placed sensor elements of 
a line. Then, three support points placed adjacent to each other in a line 
are used for ascertaining the phase relationship. 
Preferably, the reference radiation is supplied to the image forming 
optical system by a light wave guide. In another arrangement, according to 
the invention, the reference radiation to be produced is disposed so that 
it shines through an aperture plate having one, or preferably two, 
apertures arranged in, or in front of, the image forming optical system. 
The reference radiation may also be produced to shine through an optical 
wedge or prism arranged in front of the image forming optical system, such 
wedge covering a part, and more particularly, half of the image forming 
optical system. This method has become known as the "shearing method" and 
is used for deformation measurements. It is described in Applied Optics, 
vol. 18, no. 7, Apr. 1, 1979, pages 1046 through 1051 (Y. Y. Hung and C. 
Y. Liang, Image Shearing Camera for Indirect Measurement of Surface 
Strains). In this latter case, the image is not formed on an 
optoelectronic sensor with the special feature that the period of the 
carrier frequency is tuned to at least three pixels, but rather, on normal 
silver emulsion photographic material. 
The reference radiation can also be produced by an optical grating placed 
in front of, or in, the image producing optical system. 
In accordance with a further arrangement of the invention, the reference 
radiation can be introduced via a ray divider into the image forming ray 
path. 
Preferably, a plurality of reference radiation beams, each with one 
predetermined preferably constant carrier frequency, are superimposed on 
the sensor with a given relative phase relationship to each other. It is 
also possible for two reference radiation beams to be superimposed. The 
reference radiation beams may, respectively, have different frequencies. 
It is an advantage if an intermediate image is produced in the image 
forming ray path. The image forming ray path thus comprises an 
intermediate image. This is made possible by having a first and a second 
objective with the first objective placed nearer to the object or body and 
the second objective placed nearer to the image plane. The intermediate 
image is formed between the two objectives. This arrangement is 
advantageous in that the first objective may be replaced without any 
difficulty. It is also possible that the first objective be in the form of 
a zoom objective. In such first arrangements, this means that the section 
of the image may be changed as required without the necessity of 
readjusting the overall disposition of the elements of the apparatus and 
the reference radiation is introduced into the principal plane of the 
second objective. 
The invention further contemplates a method for the direct phase 
measurement of radiation, more particularly, light or infrared radiation, 
which is propagated in a transparent medium, or is reflected at a 
mirror-like surface.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Referring now more particularly to FIG. 1 and the diagrammatic 
representation of the method in accordance with the invention and of an 
apparatus for performing this method, coherent radiation in the form of, 
for example, laser radiation 2, having a predetermined frequency is 
directed onto the object on body 3 having a diffusely reflecting surface 
4. 
The radiation 5 reflected by the surface 4 of the object or body 3 is 
directed by an image forming optical system 6 to form an image in an image 
plane 7. In the image plane 7, there is a sensor 8 with a plurality of 
regularly arranged sensor elements 9 as shown in FIG. 2. The sensor may be 
a CAD sensor or a CAD matrix. Currently available sensor elements have a 
density of approximately 100 sensor elements referred to as pixels per mm 
on the sensor. 
The sensor 8 is also irradiated by a reference radiation source 10 with 
reference radiation 11 having a predetermined and preferably constantly 
carrier frequency with a given phase relationship. The frequency of the 
reference radiation is preferably exactly the same as the frequency of 
radiation 2. 
The image forming optical system 6 is preferably designed and set so that 
the images of the speckles produced by radiation 2 on the surface 4 of the 
object or body 3 cover at least three sensor elements 9 in the image plane 
8, as may be clearly seen in FIG. 2. The speckle 12 shown there covers at 
least three sensor elements 13, 14 and 15. On the basis of the intensity 
signals of the at least three sensor elements, it is possible to ascertain 
the phase of the radiation 5 from the surface 4 of the object or body 3 
using a computing unit (not shown). 
As may be seen from FIG. 2, the sensor elements are arranged in parallel 
lines with equal spacing thereof. The image forming optical system 6 is 
designed and set so that the images of the speckles produced on the 
surface 4 of the object or body 3 by radiation 2 cover at least three 
adjacently placed sensor elements 13, 14 and 15 in a line in the image 
plane 7 (FIG. 1). 
FIG. 4 shows diagrammatically the intensity I. 
Due to the interference of radiation 5 coming from the surface 4 of the 
object or body 3 with the reference radiation 11, the variation in 
intensity I indicated in FIG. 4 is produced. A full oscillation of the 
intensity I extends over at least three sensor elements 21, 22 and 23 as 
shown in FIG. 4. The three sensor elements 21, 22 and 23 may thus be used 
as support points for determining the phase relationship which is 
determined or calculated from the intensities of the three sensor elements 
21, 22 and 23. Thus, the three sensor elements placed alongside each other 
give a value for the phase relationship. The method is then repeated with 
the sensor elements 22, 23 and 24 as support points for ascertaining the 
next phase relationship. Thus, it is in this manner that a line of 
progress is made and then a step is taken from one line to the next. 
In FIG. 3, the image forming optical system 6 is shown in more detail with 
the radiation coming from the surface 4 of the object or body being caused 
to form an image in the image plane 7 by the image forming optical system 
6. 
The diameter D of the objectives 6 and the image distance z are selected so 
that together with the wave length L of the radiation the diameter d of 
the speckle produced is so large that it covers at least three sensor 
elements. 
In FIG. 5, the image forming optical system 6, as shown, has a light wave 
guide 31 passing there through. It is this light wave guide which produces 
the reference radiation. 
On the other hand, in the image forming optical system shown in FIG. 6, an 
aperture plate 32 provided with a plurality of apertures 33 and 33' is 
disposed in front of the objective 6 and the reference radiation is 
produced using this plate. 
FIG. 7 shows another example for the production of the reference radiation. 
In this embodiment, there is an optical grating 34 located in front of the 
objective for producing the reference radiation. 
In the working example of the invention shown in FIG. 8, an optical wedge 
or prism 35 is placed in front of the objective 6 so that the prism covers 
over the upper half of the image forming optical system 6. Thus, the 
so-called "shearing method" is employed in the embodiment illustrated in 
this Figure. 
In FIG. 9, an arrangement for phase measurement in connection with 
transparent objects is shown which is basically suited to the measurement 
of phase when the objects are provided with a mirror-like surface. As 
shown there, after beam splitting of the reference beam 37 in the beam 
spitter 38, coherent radiation originating from a laser diode 36, is 
spread out using a telescopic lens arrangement 39. The beam, as spread 
out, passes through a sample 40, that is an object or body, in which it 
undergoes a phase shift due to a change in the refractive index caused by 
changes in temperature, pressure or concentration. An image of sample 40 
is then formed by objective 41 on sensor 42. The object light or beam 43 
on sensor 42 has the reference beam 37 superimposed thereon, such 
reference beam 37 being coupled into it through, for instance, a mirror 44 
or like means via light wave guide 45. 
If a translucent plate is arranged in the object beam, diffuse radiation 
results, which is then used for image formation in such a manner that the 
speckles cover over at least three sensor elements, as explained in more 
detail below. 
FIG. 10 shows an image forming optical system with the formation of an 
intermediate image. Radiation coming from the surface 4 of the body or 
object 3 first passes through a first objective 51 placed nearer to the 
object or body 3 and then through a second objective 52 placed nearer to 
the image plane 7. The intermediate image is formed at 53 between 
objectives 51 and 52. The reference radiation 54 is introduced in the main 
plane 55 of the second objective 52 nearer to the image plane 7. The first 
objective 51 is a replaceable objective or a zoom objective. As a result, 
the section of the image may be selected quite freely without readjustment 
being necessary. 
In FIG. 11, showing an apparatus provided with a beam splitter, the 
reference radiation 11 is introduced via a beam splitter 56 into the beam 
path between the surface 4 of the body or object 3 and the image plane 7. 
The beam splitter 56 is located in the beam path in front of the image 
forming optical system 6 and a further optical system 57 is located in the 
beam path of the reference beam 11 in front of the beam splitter 56, the 
optical system 57 being a collecting lens.