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BACKGROUND OF THE INVENTION
The present invention relates to interferometers of the type to be used for
detecting surface deformations and medium inhomogeneities.
The art of interferometers is fairly well established. The "textbook"
variety of interferometers goes back, basically, to Michelson and consists
of a light beam, a beam splitter directing components of the beam towards
two mirrors and recombining the two reflected beams to obtain an
interference pattern which can be used for a variety of purposes including
the detection of flaws in one mirror while using the other one as a
reference. The two beams have propagated along different paths, and any
resulting interference pattern is attributable to optical path
differences. The resolution of detecting surface deformations in this
manner is inherently limited by the wave length of the radiation used, one
does not obtain a finer contour pattern than permitted by the resulting
fringes whose spacing is directly related to the wave length. The spacing
of two fringes represents an elevational difference equal to one-half wave
length. The present invention relates to an interferometer which still
employs the basic principle of beam splitting, separate reflection on test
and reference mirrors, and recombining the two reflected components for
purposes of interference. However, the invention is directed towards an
attempt to obtain a higher resolution; i.e. to overcome the apparently
inherent limitation of a one half wave length resolution of the known
methods.
Other types of interferometers are known such as the Fizeau interferometer,
or the Twymann Green interferometer which really is an outgrowth of the
Michelson device. Fairly recently, one of us took a still different
approach using beams intersecting in an interference zone in which the
test object (mirror) has been placed and back scatter is observed (U.S.
Pat. No. 4,030,830) for purposes of detecting local surface defects. The
same principle of intersecting interfering beams is also used in other
applicatons (see "Optical Engineering", Vol. 15, No. 2, page 146; Lateral
Interferometry, Its characteristics, Technology And Applications). The
present invention does not follow that approach.
It should be mentioned that there is a significant need for a high
resolution interferometer for detecting small deviations from ideal
surface shapes in mirrors which are to be used in demanding applications
of modern optics. Optical devices which are limited to a one-half wave
length resolution are inadequate for that purpose. Moreover, the known
interferometer of the Michelson family are susceptible to errors on
account of vibrations of and in the equipment. Further, it is desirable to
obtain the desired information about surface deformations or medium
homogeneities in a manner permitting direct and immediate acquisition of
optical, interferometer information by electronic equipment to further
permit the direct presentation of such information as digital signals.
DESCRIPTION OF THE INVENTION
It is an object of the present invention to provide a new and improved
interferometric method and system for obtaining a representation of the
surface contour of a mirror or a description of medium homogeneity with a
resolution which is higher than given by the wavelength of the radiation
employed in the method and system. The method and system should also be
highly insensitive to physical motion of the mirror and/or of the
equipment during the measurement. The method and system is expected to be
amenable to a high degree of automation without requiring high skills in
optics.
In accordance with the preferred embodiment of the present invention, it is
suggested to produce a monochromatic beam and separating the beam into two
components. These two components are frequency shifted, but by different
amounts, and they are also orthogonally polarized. The two components are
recombined to establish a test or inspection beam which includes the still
two coherent components traveling together but (a) differing in frequency,
the difference being many orders of magnitude smaller than the frequency
of either components, and (b) having different polarizations for purposes
of identification; this will be called "tagging" in the following. This
test beam is passed into a beam splitter designed to separate the two
tagged components an directing them towards two mirrors, one being a
reference mirror, the other one being either a mirror to be tested or a
mirror disposed behind a medium to be inspected as to homogeneity. The
reflected beams are recombined and the resulting combination beam is
polarization-processed to now obtain components of the same polarizations
so that the components are permitted to interfere. Interference fringes
can be observed either visually or electronically in a plane intersecting
the latter composite beam in which fringes move in directions
perpendicularly to their extensions at a rate equal to the difference in
frequency of the two beams. Consequently, the light intensity oscillates
in any point in that detection plane and at that frequency but at a phase
that can be directly related to the optical path difference for that
point. The oscillations are detected in each of the points in the
detection plane and compared with a reference oscillation. The phase so
detected is directly proportional to the optical path difference as
between the test arm and the reference arm of the interferometer, the
optical path difference being either the result of a test surface
deformation (as compared with the surface of the reference mirror) or the
result of a local inhomogeneity of the test medium. The resolution of the
detection of optical path differences is determined by the resolution of
detecting different phase differences for different detection points in
the detector plane. Detection of the phase information in as many points
in the detection plane as practicable permits the generation of a contour
map whose resolution is no longer limited by the optical wave length
involved, but is limited only by the resolution of the point-by-point
detection process.
DESCRIPTION OF THE DRAWINGS
While the specification concludes with claims particularly pointing out and
distinctly claiming the subject matter which is regarded as the invention,
it is believed that the invention, the objects and features of the
invention and further objects, features and advantages thereof will be
better understood from the following description taken in connection with
the accompanying drawings in which:
FIG. 1 is a block diagram of a system in accordance with the preferred
embodiment for testing the figure of a mirror;
FIG. 1a is a modification of the system of FIG. 1 adapted for resting
medium homogeneity;
FIGS. 2, 2a, 2b, are plots of fringe patterns as they may appear in the
system of FIG. 1;
FIG. 2c is a signal diagram relevant to FIG. 2a;
FIG. 3 is a modification of a portion of the system in FIG. 1; and
FIG. 4 is a representative example of a contour diagram that has been
obtained with the system shown in FIG. 1.
Proceeding now to the detailed description of the drawings, the block
diagram of FIG. 1 includes an electronic-optical preparatory section 10
for producing a composite test beam having two components which differ in
frequency and polarization, an interferometric measuring section 30 and an
electronic acquisition and evaluation section 50. The purpose of this
assembly is to ascertain the surface contour of a mirror 40 and to detect
any surface defects, unevennesses, etc. Mirror 40, in effect, becomes
temporarily incorporated in section 30.
Beginning with section 10, it includes a master oscillator 11 producing a
constant frequency signal of a frequency f.sub.a. This frequency may fall
within a range typically from 30MC to 50MC; and typically f.sub.a may be
40 MHz. As will be apparent below, this frequency is produced merely as an
auxiliary operating parameter and does not become directly an operating
parameter of the interferometric measurement.
A second oscillator 12 is provided to produce a frequency which for reasons
of convenience may be called a difference frequency .DELTA.f. This
frequency may fall within the range from 0 to 20MC; typically .DELTA.f
will be 0.1 MHz. It may be advisable in cases to render the frequency of
oscillator 12 adjustable, permitting adjustment to very low values if
visual inspection of fringe patterns is desired, otherwise .DELTA.f should
be in a range in which available equipment can be used for purposes of
phase detection. This frequency .DELTA.f is a significant operating
parameter and is characterized by the fact that the value is low as
compared with the other operating frequencies in the system. A summing
network 13 plus filter receives the two outputs of oscillators 11 and 12
and produces the frequency f.sub.a .+-..DELTA.f, one of which will be
suppressed.
The basic optical input for the interferometric system is provided by a
highly monochromatic source of electromagnetic radiation, i.e. a single
frequency laser. Conveniently, this source may be a krypton ion laser 14
issuing a beam 100 of a single frequency f.sub.opt =4.59.times.10.sup.8
MHz at a wave length of 6471 A. A variable attenuator 15 establishes an
output level the amplitude of which may be varied.
The optical output of the laser/attenuator assembly is linearly polarized
but in an arbitrary plane. A .lambda./2 plate 16 is provided to adjust the
plane of a linear polarization to a suitable orientation. Presently, it
may be assumed that the plane of polarization is adjusted to extend at a
45.degree. angle to the plane of the drawing.
The radiation beam 101 as leaving the plate 16 is now received by a
polarizing beam splitter 20. The function of the splitter 20 can be taken
from its designation. First of all, it splits the incoming beam into two
components 102 and 103, preferably of equal magnitude by extracting
differently polarized components from the beam 101 and directing them into
different directions. The orientation of plate 16 as defining the
orientation of the polarization plane of beam 101 is instrumental in
obtaining the amplitude equality. Since the beam splitting is carried out
on the basis of polarization, the two beams 102 and 103 are now tagged by
specific polarization. For example, beam 102 may be polarized transversely
to the plane of the drawing and beam 103 will then be polarized parallel
to the plane of the drawing. Both beams, however, remain coherent.
Beam 102 is received by a Bragg cell 21 and beam 102 is received by a Bragg
cell 22. The Bragg cells are optically transmissive devices which upon
being electrically stimulated propagate acoustic waves in a direction
transversely to the direction of the beam propagation. These waves change
the optical density in the Bragg cell medium and in such a manner that in
additon to passing an unmodified portion of the beam each Bragg cell
diffracts some of the radiation. The relative percentage of the diffracted
intensity is proportional to the acoustic excitation of the Bragg cell.
The diffracted beam emerges at an acute angle to the principal direction
of propagation and has its frequency up or down shifted. Only one of the
latter two beams is being used as an output of each of the cells. Thus, a
frequency shifted beam leaves each of the Bragg cells at the so-called
Bragg angle, the two beams being denoted 104 and 105, respectively.
Accordingly, beam 104 is a beam of light being polarized transversely to
the plane of the drawings and having a frequency, for example. of
f.sub.opt +(f.sub.a -.DELTA.f); beam 105 is a beam of light being
polarized in the plane of the drawings and having frequency of f.sub.opt
+f.sub.a. Again, one could use the difference-of-the frequencies (e.g.
f.sub.opt -f.sub.a) which is an arbitrary choice, but the choice must be
the same for both of the two cells.
A pair of mirrors 23 and 24, respectively, redirects the two beams 104, 105
into a polarizing beam combiner which, by virtue of the specific
polarization causes beam 104 to be reflected by 90.degree. while
permitting beam 105 to pass so that a combination beam 106 leaves splitter
25. The two beams are still coherent though having slightly different
frequencies, the difference being equal to .DELTA.f; however, the two
beams are now distinctly identified and they do not interfere on account
of their different, orthogonally oriented polarizations. This beam 106 is
the output beam of the section 10.
A mirror 26 directs the beam 106 into the interferometer measuring section
30. The input of that section, therefore, is a beam having the properties
as listed above. Since the beams as considered thus far have a transverse
width which is basically established by the rather narrow output beam
waist of laser 14, an expansion of the beam is required. One could widen
the beam at this point to the dimension of the mirror 40 to be tested;
however, the optical equipment still needed for processing the beam before
undertaking the measurement would become needlessly wide and very
expensive. A widening of the beam at this point is, therefore, needed only
commensurate with the required spatial resolution of the detection, as
will be described below. Accordingly, a first beam expander 31 is provided
in the path of beam 106, providing a wider beam 107 still being of the
composite nature as aforedescribed. Beam 107 may, for example, be widened
to about 1" diameter.
The principal element of the interferometer is a third polarizing beam
splitter 32 which separates again the two expanded beams into component
beams 108 and 109 of different frequency and polarizations. Beam 108 is
directed into the reference arm or branch of the device, passes a
so-called quarter wave plate 33 to become circularly polarized and is
intercepted by a reference mirror 35 having a surface figure of very high
optical quality. The beam is reflected, returns on its incoming path and
again is linearly polarized, but now the polarization vector is 90.degree.
rotated with respect to the initial polarization so that the return beam
of 108 is reflected by the beam splitter 32 towards its forth port and
becomes one component of an output beam 110.
The beam 109 is the test beam proper and passes likewise a .lambda./4 plate
34 to become circularly polarized. A second beam expander 36 expands the
beam 109 laterally to the dimensions of the mirror 40 to be tested, or at
least to the dimensions of the area of the mirror to be tested in one test
run; for example, up to 4" or 6". The expanded beam is reflected into
itself and the reflected wave fronts (of equal phase) are spatially
modulated in the direction of propagation and in accordance with the
surface contour of the mirror 40 whereby this phase shift, in space, is
twice the depth variations of the mirror on account of the fact that any
increment of the test beam traverses any path increment twice.
The return beam of 109 is contracted by device 36, and is linearly
polarized by plate 34; the final polarization is perpendicular to the
original one of that beam. Thus, the return beam of 109 passes the
splitter 32 straight through and becomes the second component of composite
beam 110. This beam 110 is now composed of a first component having (a)
the frequency f.sub.opt +f.sub.a ; (b) a polarization transversely to the
plane of the drawing, and (c) planar wave fronts commensurate with the
planarity of reference mirror 35. The second component of beam 110 has (a)
a frequency of f.sub.opt +f.sub.a -.DELTA.f; (b) a polarization parallel
to the plane of the drawing, and (c) a wave front that is spatially
modulated by the surface irregularities (if any) of mirror 40.
This composite beam 110 after leaving the exit port of splitter 32, is
passed through a linear polarizer 37 oriented at 45.degree. to both of the
existing polarizations. This polarization filter 37 extracts from each
beam component a particular component of identical polarization. The
resulting two beams are, therefore, permitted to interfere, resulting in a
beam which can be called an interference beam. An interference pattern can
be picked up in any plane intercepting the beam path, such as the plane
42. Since the interfering waves do not have the same frequency, the
interference pattern can be described by the equation S=S.sub.o cos
2.pi.[.phi.(x,y)+.DELTA.ft]. The function .phi.(x,y) in this equation has
the following meaning. Take any point x,y in the detection plane, and
project it back through the optical equipment to mirror 40 and also to
mirror 35. .phi.(x,y) for that point represents the difference in the
length of these two optical paths. If both mirrors are truly plane (or
have the same curved contour)=const. If 35 only is plane, the function
.phi. represents (twice) the surface contour of mirror 40 in units of wave
lengths; S.sub.o is constant if the beams have constant intensity across
the width. The interference pattern, therefore, is a time variable one,
with a phase which directly represents the contour or figure of the test
mirror, or a deviation of that mirror from the contour or figure of
reference mirror 35.
A signal detector 41 is disposed in plane 42. The detector has a rather
small aperture and can be moved in the detection plane 42, for example, by
means of a motor driven cross slide arrangement 43 or the like which
establishes individual scanning positions in accordance with an array of
raster points in plane 42 for purposes of detection.
FIG. 2 is a representative example of a fringe pattern as it could be taken
from plane 42 and as it could be seen; for example, if a simple reflective
medium were placed in that plane. Such an image could also be seen by an
observer when looking from the back at a translucent plate, e.g. a frosted
glass plate when placed in that plane 42. Normally, such direct image
producing device is not present in plane 42, rather the detector 41 looks
at a very limited portion of the radiation in the traversing plane 42 but
covers stepwise an inspection field such as delineated by circle 45 in
FIG. 2. Arrows 43a and 43b depict the displacement the detector 41
undergoes in the plane 42 (being the plane of the drawing of FIG. 2) when
moved by the cross slide 43. Details of the detection process in field 45
will be discussed below, but it will be appreciated that by stepping the
position of detector 41 systematically through field 45, one obtains a
raster covering the fringe patterns.
The output signal of the detector 41 fed to a phase detector 51 as one
input thereof. The second input for the phase detector is derived from a
detector 27 which has a fixed position in the detection plane 42,
preferably near the border of the inspection field, simply to avoid
interfering with the scanning operation of the mechanically moved detector
41. As will be explained in detail below, the outputs of detectors 27 and
41 are r-f signals with an oscillation frequency .DELTA.f, but these
signals may differ in phase. Thus, the output of circuit 51 is a d.c.
signal which represents the phase between the reference signal and the
detector signal.
The output of electronics 51 is fed to a digitizer 52 feeding digital data
to the CPU 55 of section 50 which constitutes a computing and ditial data
processing facility. The CPU 55 cooperates with a memory 54 to obtain
stepwise acquisition and storage of the plane data and to execute the
acquisition program. This acquisition program includes the stepping of
cross slide 43 through the raster points in the detection plane and the
area delineated by 45. Accordinly, the facility 50 may issue drive signals
via a digital-to-analog converter 53 for operating the cross slide drives
which position and reposition the cross slide 43 and the detector 41
thereon. The control may be somewhat more complex and may include feedback
and accurate position measuring devices, etc. However, such devices are
well known and do not require elaboration. Generally speaking, devices to
position an object very accurately (e.g. detection and pick up device) are
known and can be used in this environment.
In addition, the facility 50 correlates the coordinates of the raster
points as established by the cross slide and detector 41, but being
software assigned as position data, with the phase data subsequently
acquired and taken from the phase detector 51. The facility 50 may convert
these phase data into elevation points in an x, y, z coordinate system.
These data may be printed out and/or plotted in a manner known per se in
computer technology which does not require elaboration. Reference numeral
56 refers to suitable output devices. FIG. 4 is a representative example
of such a contour map which has been plotted from data actually
ascertained with the inventive system.
It should be mentioned that automation of the operation is convenient and
practical, and the interferometer of the invention is particularly
designed to permit such automation. However, the data can be acquired
manually, for example, by moving the detector 41 into the different
position through operation of high precision adjustment spindles, and
reading the phase difference from an instrument connected to the output of
circuit 51.
After having described the system, the following summary may be in order.
The section 10 produces a composite beam (106) in which two beams of
slightly differing frequencies (the difference being .DELTA.f) and of
orthogonally oriented linear polarizations are combined in the same
optical path. Section 10, therefore, has the function of generating two
highly monochromatic, tagged beams of slightly different frequencies. The
frequency f.sub.a plays an auxiliary part only in that Bragg cells are not
commercially available at the desired rather low frequency .DELTA.f, so
that the laser beam frequency cannot be directly shifted in frequency in
that manner. The frequency f.sub.a, therefore, is provided only for
placing the frequency shift into a range that can be handled by Bragg
cells, and, as outlined above, the desired frequency difference comes
about by using two Bragg cells operating at different frequencies, the
difference being .DELTA.f. The main purpose of using frequencies .DELTA.f
which are one or two orders or magnitude lower than the frequencies at
which conventional Bragg cells operate, is to simplify the phase sensing
electronic circuits. Therefore, .DELTA.f should be below about 5Mc for
practical reasons of signal processing and phase detection. A second
purpose would be to permit setting .DELTA.f to low values including
approximately zero for purposes of visual observation. As stated, 100 KHz
is a very convenient frequency for most applications, particularly the
automated acquisition of data.
The section 30 generates an interference pattern by means of which one can
determine the planarity of the mirror 40 in a manner to be described more
fully below. The interference pattern appears in plane 42 which is
orthogonal to the direction of propagation of composite beam 110. The
pattern can be described by the function S=S.sub.0 .times.cos
2.pi.[.phi.(x,y)+.DELTA.ft], wherein the phase .phi. is directly related
to and describes the surface contour of mirror 40. The coordinates x and y
are coordinates in the plane of mirror 40 and/or in the plane 42. The
transformation in coordinates is given by the beam expander 36. Since the
function above is time variable, the interference pattern is, in fact, a
moving one in which fringe lines propagate orthogonally to their
extensions in plane 42. The detection process covering the inspection area
(45) and the plane 42 where intersecting beam 111 will produce a very fine
resolution elevation pattern representing the surface contour of mirror
40.
Section 50 actually processes the detection data to obtain such a contour
map. The input of section 50 references the function S against a function
whch could be described a R=R.sub.0 .times.cos (2.pi..DELTA.ft). This
function R is the reference signal produced by detector 27 and is used to
eliminate the time variation for purposes of directly finding .phi.=.phi.
(x,y), being a phase distribution function from which one may draw
directly a contour map such as shown in FIG. 4. To say it differently, the
detectors 41, 27 together establish time varying functions which together
describe the interference pattern and which include the spatial
distribution of the contour of the test mirror as phase information. The
phase detection extracts that phase information, separately for each
raster point and permits, in turn, the generation of a contour map.
The polarization type beam splitting arrangement 32, 33 and 34 is used for
efficiently splitting the beam into the two polarized components. In
principle, one could use a regular beam splitter with polarization filters
placed in each arm. However, on each passage, one would lose 50% beam
intensity (or a total of 75%) and the resolution would suffer.
Other modifications which are conceivable relate to the scanning and
detection device 41/43. Instead of the electromechanical type scanning and
physical movement of the detector, one could use electronic imaging
equipment with electron beam type scanning or one could use a detector
array composed of semi-conductor elements which are being scanned and
interrogated individually. In this instance, one of the cells in the array
will serve permanently as reference signal detector.
In all these instances, however, the scanning process should be under
control of the computer 50 because it is absolutely essential to correlate
raster point identification with acquired phase data. However, the
scanning unit may be autonomous and may furnish the position data to the
acquisition electronics 50.
In order to more fully understand the detection process, several different
situations will be discussed. Assuming in the first instance, (a) that
.DELTA.f=O, both beam components (104, 105 or 108, 109) having equal
frequency and (b) that test mirror 40 is indeed absolutely plane, i.e. has
no defect. Under such conditions both components in beam 110 are
everywhere in phase or have a constant phase difference in the plane 42 or
in any plane parallel thereto; they interfere and produce a uniform
brightness in the detection field of plane 42. If one would shift one or
the other of the mirrors 35, 40 in the respective direction of the beam
paths the brightness changes in the detector field. Upon shifting one or
the other of the mirrors from a position in which the resulting brightness
is very low, and over a distance equal to .lambda..sub.opt /2 the overall
brightness would change through a full cycle, e.g. from dark to maximum
brightness and back to dark.
The second instance assumes either a very large unevenness or a slight tilt
of mirror 40 which is the equivalent of a large, uniform unevenness of the
mirror. In this case now, plural parallel interference fringes in the form
of straight lines will appear in the detection plane 42. The line pattern
will exhibit a line spacing which is inversely proportionate to the
inclination or the assumed large unevenness of the mirror 40; the line
spacing is also linearly proportionate to the wave length. We still assume
.DELTA.f to be zero, and the fringe line pattern is stationary. These
interference fringe lines, their contour and their spacing represent the
mirror surface. FIG. 2 can be interpreted as an example for this case. It
should be pointed out, however, that for purposes of the step-by-step
explanation, we ignore the detection process presently.
If now the unevenness is an irregular one (assumed case 3), these fringe
lines delineate the contours of the unevennness as contour lines and the
spacing of the lines represents the steepness. The solid lines in FIG. 2b
represent that case. The contour line resolution of detecting optical path
differences is one-half of the chosen optical wave length. To produce this
result (.DELTA.f=0) one actually does not need the different polarizations
as the device would, in fact, operate just as a regular, conventional
interferometer.
Case 4 assumes that the test mirror 40 is planar, i.e. highly flat, and not
tilted, but .DELTA.f.noteq.0, the overall brightness will fluctuate
spatially, uniformly over the entire detection zone and at the frequency
.DELTA.f.
Next, case 5, we turn to an instance of a slightly tilted planar (or
uniformly uneven) test mirror 40. In the case 2 above, a fringe line
pattern appeared that was stationary for .DELTA.f=0. As a consequence, the
line pattern will run everywhere in a direction extending transversely to
the extension of the lines and at a rate that is equal to .DELTA.f.
Consider the following. A plane exactly at right angles to beam 109 may be
regarded as horizontal as far as the mirror is concerned and a direction
toward the mirror may be "down" and the opposite direction could be termed
"up". A tilt of mirror 40 will, therefore, have one edge 37 up" and one
edge "down". The frequencies may have been chosen so that the fringe lines
will, in fact, run "down hill". Now we turn to other types of defects.
Take the case of a depression, i.e. dent in the mirror surface, the
contour lines will be more or less concentric around the deepest point of
the dent and all lines moving towards that bottom of the depression will
appear to vanish therein. In the case of a bulge or buckle in the mirror
surface, the contour lines will "appear" at the peak and run "down hill"
in all directions as ever widening closed lines.
Thus, the running of the fringe lines represents in sequential instants
different sets of contour-fringe lines to represent the unevenness of the
mirror 40. The pattern is the same for instants being apart by one full
(or integral multiples of one) oscillation period of frequency .DELTA.f.
To state it differently, a set of fringe lines will be present in plane 42
in any instant and the lines are spaced apart from each other commensurate
with a total (round trip) optical path difference equal to
.lambda..sub.opt from line to line. An instant being later by, say 1/10 of
an oscillation period at the .DELTA.f frequency, the contour line pattern
has shifted in that each line has, so to speak, migrated down to a level
.lambda..sub.opt /10 below the respective previous levels. 1/10 (or 1/100
or 1/1000) of a period .DELTA.f later the lines have shifted again down by
.lambda..sub.opt /10 (.lambda..sub.opt /100 or .lambda..sub.opt /1000).
FIGS. 2a and 2b represent such cases. The solid drawn lines are assumed
fringe lines of minimum brightness (at enhanced contrast) representing the
interference pattern in a given instant. The dashed lines represent the
same fringe line pattern but about 1/10 of the .DELTA.f oscillation period
later.
Each pattern represents a contour map of the mirror at a .lambda..sub.opt
elevational resolution, but many such patterns together, i.e. a
(hypothetical) set of lines drawn at sequential instants, but now taken
together, represent the contour of the mirror's unevenness at a much
higher resolution. Thus, if one were to take a plurality of snapshots, say
10 or 100 per oscillation cycle of .DELTA.f, one could obtain ten or one
hundred different fringe line patterns which upon being superimposed,
would be a contour map representing the mirror's unevenness at a ten or
hundredfold increased resolution. Hypothetically, one could produce an
output in this manner, but the scanning process of the equipment as
described, is more elegant and of better immediate usefulness, though
being basically electrically equivalent of the foregoing "superimposed
multiple snapshot" method.
It can readily be seen that the light intensity in any one particular point
in the detection plane 42 will oscillate at the .DELTA.f frequency as the
fringe pattern passes across (FIG. 2c). Such a point (.e.g. 41') represent
a particular point on mirror 40, and the phase of that oscillation as
detected in relation to the phase of similar oscillation in a neighboring
point (e.g. 41" in FIG. 2a) represents the relative elevation or
depression of these two points in relation to each other, their "altitude"
difference. The upper and middle lines in FIG. 2c represent these
oscillations, and the phase difference .DELTA..phi. is directly
proportional to the elevational difference of the two points 41', 41" as
projected back onto mirror 40. However, rather than relating the phases of
the oscillations in any point in field 45 to the phase of a neighboring
point, it is more practical to detect the phase of oscillation in any of
the points in inspection area or field 45 in relation to a reference which
can be used for any and all such points in the detection plane. This is
the function of phase detector 51 as receiving a reference signal from the
detector 27.
It will be recalled that detector 27 extracts the .DELTA.f frequency at a
particular phase from beam 106, and circuit 51 determines the phase (as a
d.c. voltage signal) between that reference and the particular oscillation
monitored by detector 41 in any instant and for any particular point in
the detection field 45. The lower line of FIG. 2c represents the reference
oscillation and .DELTA.'.phi. is a phase difference that is representative
of the local contour of the mirror 40 relative to the point on the mirror
which is the projection of the location of the reference detector 27.
The accuracy of these detection proceedings are, of course, dependent upon
the dimensions of the input aperture of detector 41 which will not sense
any intensity oscillations in a point but necessarily over a finite area.
Thus, strictly speaking, it was not quite accurate to speak of raster
points, rather one should speak of an areal raster element, though the
center of that area could be deemed to define a raster point. The larger
the raster area, the less pronounced will be the oscillations that can be
detected, and an aperture about equal to any spacing of the fringe lines
will not perceive any brightness oscillations. Thus, the detector aperture
should be samll as compared with the fringe line spacing (see FIG. 2). It
should be noted, however, that the raster points (defined e.g. as the
center of the detector aperture) may well be spaced from each other at a
distance less than the detector aperture width, i.e. incremental areas
under inspection by detector 41 as far as sequential inspections are
concerned may overlap. Each such raster point yields a particular phase as
to the detected oscillation at the .DELTA.f frequency, and the phase value
is directly indicative of a relative elevational value of the mirror at
that spatial point of the raster scan. The phase values together define
the mirror figure at a spatial resolution that is given by the raster
point spacing; the resolution is not dependent upon the auxiliary
modulation frequency f.sub.a and is only insignificantly dependent upon
the frequency .DELTA.f and the value for .lambda..sub.opt.
The phase values as so established are not unambiguous but require
modification and augmentation. The elevational pattern as established on
the pass of such multiple raster points can be deemed divided by
hypothetical lines of phase angle zero. The placement and overlay of these
lines is quite arbitrary per se, but depends directly on the phase of the
output of detector 27. Thus, the location of detector 27 and the phase
line through that point represents the zero altitude level. Other such
hypothetical phase zero lines will represent contour lines at an altitude
of +.lambda..sub.opt, +2.lambda..sub.opt, +.lambda..sub.opt,
-.lambda..sub.opt, etc. The phase values detected in raster points between
such "lines" represent corresponding intermediate elevations at a
resolution depending, as stated, on the raster. Generally speaking, the
detector 41 will be stepped from raster point to raster point, and the
phase of the oscillations will be ascertained point by point. A separate
directional counter in processing facility 50 should keep track of the
phase-zero crossings and should count the even multiples of such crossings
as altitude and level units of .lambda..sub.opt each. An ambiguity in
elevation can occur here only if the elevational difference between two
raster points happens to be larger than one full wave length
.lambda..sub.opt. However, one may make the raster resolution sufficiently
fine so that this situation simply does not occur.
FIG. 4 depicts a contour map which was drawn by a plotterfor the
three-dimensional model, in an isometric view based on actual data. The
ordinate represents optical path differences and the horizontal and the
third depth dimension represent the detection plane 42. The intersections
of grid lines are the acquired elevational phase data augmented by
.lambda..sub.opt, 2.lambda..sub.opt, etc., as needed. The grid lines are
simply added as straight lines and connect phase values of adjacent raster
points. The above-mentioned phase angle zero lines would be contour lines
resulting from intersection of the contoured surface with horizontal
planes traversing the vertical axis at .lambda..sub.opt, 2.lambda. etc.
The mode of representing the surface contour of mirror 40 is a matter of
convenience. Conceivably, one could move the detector 41 into positions in
which the detected phase has particular value and on as fine a scale as
such a position control permits. Thus, rather than operating on the basis
of a fixed pattern of raster points, one could map the plane 42 in field
45 to detect equal phase points.
It should be realized that the method is not limited to the detection of
planarity of mirrors, but one will detect per se the existing contour.
This contour may, for example, be a curved one (spherical, parabolic,
etc.), and the resulting map simply depicts that contour. If the reference
mirror is likewise a curved one, e.g. having "ideal" curvature as to its
surface, then the resulting map will again merely represent the deviation
of the actual contour of the test mirror from the contour of the reference
mirror.
The method and system as described are highly invariant against error
sources. Of particular concern here are displacements, even oscillating
displacements transversely to the extension of either mirror (piston
movement). They will not produce errors because any resulting phase shift
affects detectors 41 and 27 equally. Incorrect readings could occur if
such oscillations have a frequency comparable to .DELTA.f. However,
.DELTA.f is a free parameter, and it can readily be chosen to be well
above any expected mechanical vibration frequency which any part of the
equipment involved may undergo.
Conceivably, one may define the reference phase differently. For example,
one may use the output of oscillator 12 rather than optically extracting
the .DELTA.f reference signal. Still alternatively, one could optically
extract (via a polarization filter) a reference signal of .DELTA.f
frequency directly from beam | | |
