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Description  |
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The present application relates to the detection of the angle of a beam of
light.
Systems for detecting the angle of a beam of light are used, for example,
in devices for detecting the alignment of two parts of an apparatus or for
detecting the flatness of an optical table or other table by measuring the
relative alignment between different portions of the table. Similarly,
they may be used for measuring the flatness of an optical slideway or of a
machine bed.
In such systems, a beam of light is shone onto the surface the alignment of
which is to be detected, and the angle of the reflected beam is detected.
The angle of the reflected beam will provide a measure of the angle of the
surface from which it is reflected. In practice, the beam is normally
reflected not from the surface itself but from a mirror placed on the
surface, in order to ensure a high quality specular reflection.
In a known system for measuring the angle of a light beam, a parallel-sided
light beam is directed to an object and the reflected return beam is
captured by a lens. The angle of the reflected return beam is determined
by placing a multi-element photodetector spaced from the lens by the focal
length thereof. The reflected return beam will be parallel-sided, and as
is well known, a parallel-sided beam is focussed by a lens to a spot at a
position one focal length from the lens, the position of the spot in the
focal plane being determined by the angle of incidence of the
parallel-sided beam. Accordingly, this arrangement creates a spot of light
on the multi-element photodetector at a position corresponding to the
angle of the reflected return beam. The position of the spot can be
detected from the output of the photodetector.
While the arrangement described above is highly accurate in theory, it is
in practice limited by the quality of the optical elements used, and also
by the characteristics of the multi-element photodetector. If the gemoetry
is set up in a theoretically perfect arrangement, the entirety of the
light from the reflected return beam is focussed on to a single element.
The resolution with which the system can detect the angle of the light
beam will depend on the pitch of the elements in the detector. In order to
provide a good quality output signal, the elements must be able to
withstand the light power of the fully focussed beam, and preferably will
not saturate at this light intensity. In practice, the apparatus may be
set up so that the light beam is not focussed precisely to a spot on the
detector, so that the illuminated area covers more than one element. The
position of the brightest part of the illuminated area can be detected by
comparing the intensities of the signal outputs from all of the
illuminated elements. A drawback to this arrangment is that the
calculation is very dependent on the quality of the photodetector
elements. This system is adversely affected by the failure of any one of
the photodetector elements. GB-A-2129245 proposes an arrangement in which
a mask with slits allows narrow lines of radiation to fall on an array of
rows of photo-sensitive detector elements. The rows extend transverse to
the direction of the lines of radiation. Each element is as long as the
distance between the slits of the mask and shaped so that for half its
length it has a constant width and for the other half it has an
exponentially decreasing width. Alternate rows are arranged to face in
opposite directions, and the ratio of signal strength from rows facing one
way to signal strength from rows facing the other way provides a measure
of the position along the respective detector elements of respective lines
of radiation. Since this position will change with the angle of incidence
of the radiation, this ratio of signal strengths is also a measure of the
angle of incidence.
According to an aspect of the present invention there is provided an
arrangement for detecting the angle of a light beam in which a repeating
waveform pattern is created on a photodetector array, such that a feature
of the waveform, for example its shape, its wavelength or its phase,
varies with the angle of the light beam. Accordingly, the angle of the
light beam can be determined by appropriate processing of the output of
the photosensor array. Because the pattern of light formed on the
photosensor array is a repeating waveform, a relatively large number of
photodetector elements contribute to the output, so that the accuracy of
the measurement on any particular occasion is not highly dependent on the
performance of a very small number of elements in the detector array.
Additionally, the large number of photodetector elements allows a greater
total optical power to contribute to the output signal than in a system
which focusses the beam to a spot. This allows an improved signal to noise
ratio.
Preferably the pitch of the photosensor elements in the array is shorter
than half the wavelength of the waveform feature being used in processing
the photosensor output. More preferably the pitch is shorter than a
quarter of the wavelength. This short pitch allows good sampling of the
waveform property.
In order to ensure a good detection of the waveform property, it is also
preferable that the detector array should be at least as long as the
wavelength of the waveform feature of the pattern being used in processing
the photosensor output, more preferably at least twice as long as the
wavelength of the waveform and still more preferably at least four times
as long.
Depending on the way in which the repeating waveform pattern is created on
the photodetector array, its wavelength may vary with the angle of the
light beam. In this case, the pitch of the photosensor elements should be
determined with reference to the shortest wavelength of the repeating
pattern arising in the range of angles of the light beam with which the
arrangement is to be used, and the length of the detector array should be
determined with reference to the longest wavelength of the repeating
pattern arising in the range of angles of the light beam with which the
arrangement is to be used. The range of angles of the light beam with
which the arrangement is to be used (the measurement range of angles) may
be determined by a variety of factors. For example, the construction of
the arrangement may be such that if the angle of the light beam falls
outside a particular range, the repeating waveform pattern may not be
formed or may not fall on the detector array.
In the preferred embodiments of the present invention, the size of the
detector array can be expanded up to the limit of the area in which the
repeating pattern is formed, so as to increase the number of elements
contributing to the output, thereby improving the quality of the output
signal and further reducing the effect of variations in the performance of
different detector elements.
In order to analyse the output signals from the photodetector, it may be
useful to perform a Fourier transform on the output signal, for example by
using a fast Fourier transform (FFT) procedure.
In one embodiment of the present invention a beam of light the angle of
which is to be detected is caused to interfere with a reference beam, and
the interference pattern is detected by a photodetector. The pattern of
light and dark formed on the photodetector by the interference pattern
will have a periodicity, and its wavelength will depend on the angle
between the reference beam and the beam the angle of which is to be
detected.
Alternatively, the beam the angle of which is to be detected may fall onto
a photodetector array through one or more masks having a repeating
pattern, for example a sinusoidal pattern of light and dark. The masks are
spaced from one another, or where only one mask is used this is spaced
from the detector. This spacing means that the position at which the
shadow of the first mask falls on the next mask or on the detector varies
with the angle of the incident light. Where two masks are used this will
affect the shape of the waveform of the resulting pattern formed on the
detector, and in either case a phase property of the detector output will
vary with the angle at which light is incident on the arrangement.
Where only a single mask is used, this may be provided on one surface of a
block of glass or similar transparent material, and the detector array
(e.g. a CCD) may be formed on or bonded to an opposed surface, so as to
ensure dimensional stability of the arrangement.
In processing the output of the detector array, the value is determined of
a parameter which varies with the angle of the beam of light. It may be
possible to go on to apply the value of this parameter to an equation
which has been predetermined from a knowledge of the features of the
system to calculate the angle. However, it will often be more convenient
to calibrate the system by discovering the value of the parameter for
light beams of known angles, thereby to form a look-up table which the
system can use subsequently to determine the angle from the value of the
parameter extracted from the photodetector output.
Embodiments of the present invention, given by way of non-limiting example,
will now be described with reference to the accompanying drawings, in
which:
FIG. 1 shows schematically a first embodiment of the present invention;
FIG. 2 shows a schematic close-up of the detector arrangement of the
embodiment of FIG. 1;
FIG. 3 shows a processing circuit for processing the output of the
photodetector array;
FIG. 4 is a view corresponding to FIG. 1, of a second embodiment of the
present invention;
FIG. 5 is a schematic close-up view of the detector arrangement of the
embodiment of FIG. 4;
FIG. 6 shows a first physical structure for the detector assembly in the
embodiment of FIGS. 4 and 5;
FIG. 7 shows an alternative physical construction of the detector assembly;
FIG. 8 shows a further alternative physical construction for the detector
assembly;
FIG. 9 is a schematic view corresponding to FIG. 1 of a third embodiment of
the present invention;
FIG. 10 is a schematic close-up view of the detector arrangement of the
embodiment of FIG. 9; and
FIG. 11 shows a modification for the embodiments of FIGS. 1, 4 and 9 to
enable the angle of a light beam to be detected along two mutually
transverse axes.
FIG. 1 shows schematically an arrangement of parts in a first embodiment of
the present invention, and FIG. 2 is schematic enlarged view of the
detector portion of the apparatus of FIG. 1.
In the arrangement of FIG. 1, light from a light source 1 passes through a
stop 3 and a collimator lens 5 to fall on a beam splitter mirror 7. Part
of the light is reflected by the beam splitter mirror 7 to an internal
reference mirror 9, which returns it to pass through the beam splitter
mirror 7 to a photodetector array 11. Typically, the photodetector array
11 is a charge-coupled device (CCD).
Light from the light source 1 which passes through the beam splitter mirror
7 passes to an external measurement mirror 13, which is mounted on a
surface the alignment of which is to be measured. The light is reflected
from the external measurement mirror 13 back to the beam splitter mirror
7, which reflects it to the photodetector array 11. Accordingly, two beams
of light reach the photodetector array 11, one from the internal reference
mirror 9 and the other from the external measurement mirror 13. By the use
of coherent light, typically by providing the light source 1 as a laser,
these two beams will interfere with each other. The resulting interference
pattern is detected by the photodetector array 11.
Turning to FIG. 2, successive wave fronts of the two beams of light are
shown in broken lines, whereas the two beam directions are shown in
unbroken lines. The angle between the two beams is exaggerated as compared
with FIG. 1, for the purposes of illustration.
As can be seen in FIG. 2, at the positions along the photodetector array 11
which are marked with arrows in the Figure, the light from the two light
beams will interfere constructively, and accordingly the photodetector
array will be illuminated brightly at these points. These points are
determined by the locations at which the wave fronts in the different
beams cross each other. These points are the corners in the diamond-shape
pattern shown in FIG. 2. As will be appreciated, as the directions of the
two beams of light become more similar, the diamond-shapes will become
wider, and accordingly the points of constructive interference on the
photodetector array 11 will become spaced further apart.
If the angle of the reference beam or the angle of the photodetector array
11 is altered, the separation between adjacent brightly illuminated
portions on the photodetector array (i.e. the wavelength of the pattern of
light and dark on it) may vary. For a given direction of the reference
beam and orientation of the photodetector array 11, the wavelength of the
pattern formed on the photodetector array 11 will be a measure of the
angle of the measurement beam relative to the reference beam and to the
photodetector array 11.
It can be seen that the pattern formed on the photodetector array 11 will
be a pattern of alternating light and dark fringes, and that the
wavelength of this pattern will vary with the angle between the two beams
of light. As the beams of light become closer and closer to being
parallel, the wavelength of the pattern on the photodetector array 11 will
increase, and if the two waves are completely parallel this wavelength
will be infinite. Since it becomes difficult to measure the properties of
the waveform of the light and dark pattern formed on the photodetector
array 11 when its wavelength becomes very long, the internal reference
mirror 9 is provided so that the reflected beam from it is at a slight
angle to the reflected beam from the external measurement mirror 13 when
the external measurement mirror has the perfect desired alignment. In this
way, a measurable output is obtained from the photodetector array 11 when
the surface on which the external measurement mirror 13 is placed is
correctly aligned.
Conveniently, all of the parts shown in FIG. 1 except for the external
measurement mirror 13 can be provided as a unit in a common casing.
FIG. 3 shows schematically the parts of a processing circuit for obtaining
the angle of the light beam from the external measurement mirror 13 from
the repeating pattern of light and dark formed on the photodetector array
11. In addition to the detector array 11, the system of FIG. 3 comprises a
processing unit 15, including program and working memory, a look-up table
17, an optional fast Fourier transform unit 19, and an output device 21
such as a display or a printer for providing the output information
concerning the angle of the beam from the external measurement mirror 13.
The fast Fourier transform unit 19 can be provided as a software package
within the program memory of the CPU 15 if desired. Fast Fourier transform
units and software packages are well known.
There are a variety of ways in which the output signal from the CCD array
11 can be processed to obtain the desired angle information. In one simple
method, the signal is processed by the CPU 15 in a manner which is well
known, to provide a level-adjusted signal which passes above and below
zero, and the points at which the signal crosses the zero level are
determined. The wavelength of the pattern formed on the CCD array 11 can
be obtained directly from the spacing between the zero-crossing points. As
explained above, this wavelength is a measure of the angle of the external
measurement mirror 13.
In an alternative method, which is presently preferred on the grounds of
resolution and accuracy, the output signal from the photodetector array 11
is subjected to a fast Fourier transform by FFT unit 19, so as to be
transformed into the spatial frequency domain, filtered, frequency
shifted, and subjected to an inverse Fourier transform. This process can
be divided into five steps, as follows.
1) Detecting interference fringes
Let G.sub.m be the gradient of the phase front of the measurement beam at
the detector plane, and G.sub.r be that of the reference beam, and p the
phase associated with the difference in the average optical path lengths
of the two beams, the interference pattern I can be written as
##EQU1##
where a and b are real quantities and are dependent on the intensity
distribution of the light beams, .lambda. is the wavelength of the light,
and f.sub.r =G.sub.r /.lambda., f.sub.m =G.sub.m /.lambda..
Since the light beams are not infinitely wide and will not normally have a
uniform intensity across them, the beam intensity varies with distance x
along the detector array 11. Therefore the values of a and b vary with x
and for this reason a and b are shown as functions of x in equation (1).
Equation (1) can be rewritten as
##EQU2##
where j=.sqroot.-1 and "exp" means "e to the power of". The output from
the CCD array 11 would be essentially as shown in equation (2).
2) Fourier transform
Taking the Fourier transform of the output of the CCD array 11 yields
##EQU3##
where F denotes the Fourier transform operation, A and B are the
transformed functions of a and b, and f.sub.x is the spatial frequency
variable. B is obtained by applying the convolution theorem of a Fourier
transform and the sifting property of a Dirac-Delta function.
Graphically, equation (3) can be represented as a frequency distribution
having peaks at f.sub.x =-(f.sub.r -f.sub.m), 0, and +(f.sub.r -f.sub.m).
3) Filtering
This is to select either the positive or the negative parts of the spectrum
and is done by multiplying equation (3) by a filter function centred at
f.sub.x =f.sub.r and with an appropriate bandwidth sufficient to include
all expected values of (f.sub.r -f.sub.m) but exclude f.sub.x =0. The
resulting filtered spectrum I.sub.f is therefore
I.sub.f 1/2B(f.sub.x -f.sub.r +f.sub.m)expjp (4)
4) Shifting
The spatial frequency value in equation (4) is shifted by an amount equal
to f.sub.r to provide a shifted spectrum I.sub.s of
I.sub.s =1/2B(f.sub.x +f.sub.m)expjp (5)
5) Inverse Fourier Transform
Taking the inverse Fourier transform of equation (5) yields the inverse
function I.sub.o
##EQU4##
Since b is entirely real, the only phase term is contained in the
exponential function. The tilt of the measurement beam therefore is given
by the gradient G.sub.m of the linear term in the phase of the inverse
Fourier transform. Note that with an FFT routine, the resultant is in the
form of real and imaginary parts. The phase, and hence its linear gradient
can be determined easily. The angle of the external measurement mirror 13
can be obtained from the gradient G.sub.m by reference to the geometry of
the optical system.
Both in the case where the wavelength of the signal on the photodetector
array 11 is extracted from zero-crossing information and in the case where
the gradient of the linear term in the phase of an inverse Fourier
transform signal is extracted, it is theoretically possible to derive a
formula for converting the extracted signal into the angle of the external
measurement mirror 13, by knowledge of the optical properties of the
apparatus. However, it will normally be more convenient in practice to
perform a calibration operation on the apparatus after it has been
constructed, in which values of the extracted signal are determined for a
variety of known angles of the external measurement mirror 13, and from
this a table relating the value of the extracted signal to the angle of
the mirror 13 can be constructed. Such a table is then stored as the
look-up table 17, and the CPU 15 uses the look-up table 17 to obtain angle
information corresponding to the extracted wavelength value or inverse
Fourier transform phase signal value. The angle value thus obtained is
provided to the output unit 21.
Typically, a CCD array used as the photodetector array 11 may have, for
example, 2048 cells or 4096 cells, at a pitch of, for example, 10
micrometres. Thus the total length of the array will be of the order to a
few centimetres. The portion of the array on which the interference
pattern is formed may be very much longer than the wavelength of the
interference pattern as formed on the array, so that there are many cycles
of the repeating pattern formed on the array 11. Accordingly, if any
individual CCD cell fails or provides a non-standard output, this has a
very small effect on the reliability of the output angle measurement.
The zero-crossing signal processing method described above has a good
property of resisting the effects of variations in the intensity of light
across the beam. If the Fourier transform signal processing method is
used, variations of light intensity across the beam may create additional
terms in the initial Fourier transform output. However, provided that the
intensity is uniform over a distance of the order of magnitude of the
wavelength of the pattern of light and dark formed on the photodetector
array 11, such components in the Fourier transform signal will easily be
rejected.
In the arrangement of FIGS. 1 and 2 the component parts should be stable
during the measurement operation. If, for example, there was any movement
of the external measurement mirror 13 while the exposure of the
photodetector array 11 was taking place, the pattern on the photodetector
array 11 would move and so the pattern as detected would be blurred. In
order to minimise any difficulties of this type, it is preferred to have a
very fast exposure of the photodetector array 11, for example by employing
a single shot laser system in the light source 1.
As has been mentioned above, the interference-based system of FIGS. 1 and 2
requires a parallel-sided beam of coherent light. Another constraint is
that optical impurities, such as a speck of dust on one of the mirrors,
will create interference fringes which will increase the background noise
in signal read from the photodetector array 11. Accordingly, the system
must be kept clean and be operated in a clean environment.
FIGS. 4 and 5 are views corresponding to FIGS. 1 and 2, of a second
embodiment which avoids the need to create an interference pattern.
In the arrangement of FIGS. 4 and 5, a light source 1, a stop 3, a
collimator lens 5 and a beam splitter mirror 7 are provided as in FIG. 1,
except that the light from the light source 1 does not need to be
precisely parallel-sided nor coherent, and therefore a variety of other
light sources are usable in addition to a laser.
In this system, there is no internal reference mirror, light from the light
source 1 is reflected by the mirror 7 to be directed onto the external
measurement mirror 13, and the light returning from the external
measurement mirror 13 passes through the mirror 7 to the photodetector
array 11. Mounted in front of the photodetector array 11, so that the
light from the external measurement mirror 13 falls onto it, are two
shadow gratings or masks 23, 25, a distance d.sub.1 apart. The nearer mask
25 is a distance d.sub.2 from the photodetector array 11. Each of these
masks has a repeating pattern of varying light transmissivity. For
example, each mask may vary between substantially entirely transparent and
substantially entirely opaque in a sine wave cycle. This sine wave
variation in transmissivity is indicated schematically in FIGS. 4 and 5 by
the undulating line shown in each of the masks 23 and 25.
As the light reflected from the external measurement mirror 13 falls on the
photodetector array 11 through the masks 23, 25, a shadow of each mask
will be formed on the photodetector array 11. Each shadow will be an
alternating pattern of light and dark, having a waveform and a wavelength
in accordance with the mask concerned. The final pattern of light and dark
actually formed on the photodetector array 11 will be a composite of the
shadows from both of the masks 23, 25.
As can be seen from FIG. 5, a ray of light which passes through one
particular point on the first mask 23 will pass through a point on the
second mask 25 which is determined by the angle of the ray of light. In
FIGS. 4 and 5 the masks are shown as having patterns of the same
wavelength, and in phase with each other for light perpendicular to the
masks and the photodetector array 11. The superimposition of the shadows
of the two masks 23, 25 will create a pattern of light and dark on the
photodetector array 11 having a formula which is the product of
multiplying together the formulae of the two masks 23, 25. The masks will
be multiplied together without any offset if the direction of incident
light is perpendicular to the masks 23, 25 and the photodetector array 11.
However, where the light is angled from the perpendicular the formulae of
the masks will be multiplied together with a distance offset equal to
d.sub.1 tan a where a is the angle between the direction of the light and
the perpendicular to the masks 23, 25, and the product will itself be
offset relative to the photodetector array 11 by d.sub.2 tan a. These
distance offsets will represent phase offsets in the equation for the
masks, according to what proportion of the wavelength L of the mask
pattern is represented by each distance offset.
If the position or angle of the masks 23, 25 or the photodetector array 11
is altered, the phase offsets in the signal read from the photodetector
array 11 may also alter. For a given arrangement of the masks 23, 25 and
the photodetector array 11, the phase offsets in the signal read from the
photodetector array 11 will be a measure of the angle of the measurement
beam relative to the masks 23, 25 and the photodetector array 11. The
wavelength of the pattern of light intensity formed on the photodetector
array 11 is determined by the mask patterns, and does not vary with the
angle of the beam of light.
If the transmissivities T1 and T2 of the masks 23, 25 are both given by:
T1=T2=1+cosX (7)
where X is the normalised distance along the masks 23, 25, (i.e. X=2.pi.
where the distance is one wavelength L of the mask pattern) the pattern of
light S on the photodetector array 11 is given by:
##EQU5##
where K.sub.1 is the phase offset between the shadows of the patterns of
the masks 23, 25 resulting from the slant of the light, and K.sub.2 is the
phase offset of the shadow of the pattern of the nearer mask 25 on the
photodetector array 11. The phase offsets K.sub.1 and K.sub.2 are related
to the spacings d.sub.1 and d.sub.2 by the formulae:
k.sub.1 =(2.pi.d.sub.1 tan a)/L (9)
k.sub.2 =(2.pi.d.sub.2 tan a)/L (10)
where a is the angle by which the light differs from the perpendicular to
the masks 23, 25, and L is the wavelength of the transmissivity pattern of
each of the masks 23, 25.
Multiplying out equation (8) gives:
S=1+cos (X+k.sub.2)+cos (X+k.sub.1 +k.sub.2) +cos (X+k.sub.2). cos
(X+k.sub.1 +k.sub.2) (11)
and applying trigonometric identities gives:
##EQU6##
It can be seen that the phase offset k.sub.1 appears in the dc offset level
of the output of the photodetector array 11 and the amplitude of the first
harmonic (cosX) term, and both the phase offsets k.sub.1 and k.sub.2
appear in the phase of both the first harmonic (cosX) and the second
harmonic (cos2X) terms.
If a fast Fourier transform is performed on the output of the photodetector
array 11, the output will be in the form of the amplitude of the dc
component and the amplitude and phase of the harmonics. Since the phase
information depends on (k.sub.2 +k.sub.1 /2), the conversion of this into
information about the angle a depends on the values of both d.sub.2 and
d.sub.1. If the amplitudes of the dc component and the first harmonic are
used, the conversion of this into information about the angle a depends
only on the value of spacing d.sub.1, and the precise value of d.sub.2
does not matter.
As described above with reference to the first embodiment, the information
obtained by Fourier transform processing is most conveniently converted
into information relating to the angle of the light beam by reference to
the look-up table 17, compiled by a calibration process.
As can be seen from equation (9), for any given value of the angle a, the
value of k.sub.1 is directly proportional to the separation d.sub.1
between the two masks 23, 25. Therefore the sensitivity of the device can
be increase by increasing the spacing d.sub.1. However, this will also
reduce the range of angles of light for which the apparatus can be used,
since any value of k.sub.1 outside the range +.pi. to -.pi. cannot be
distinguished from a corresponding value inside this range. Accordingly
the device should only be used to detect angles inside this range, unless
some further arrangement is provided to distinguish between different
angles resulting in the same phase offset k.sub.1.
For a CCD array as previously described with reference to the first
embodiment, the separation d.sub.1 between the masks 23, 25 will
conveniently be around 4 to 5 mm, although it can be up to about 5 cm. The
separation d.sub.2 between the photodetector array 11 and the closer mask
25 can conveniently be a few mm, or up to about 5 cm.
In the example described above, the patterns of the two masks 23, 25 had
the same frequency and were in phase. This is not necessary, but if they
have different frequencies there will be additional terms in equation (12)
above. In this case, the processing circuit of FIG. 3 should identify and
separate out the terms in the Fourier transform output which vary with the
angle a.
For the CCD type and mask spacing given above, the wavelength of the
repeating transmissivity pattern of each mask will typically be of the
order of 50 .mu.m. As a general constraint, the wavelength of the mask
pattern should be greater than the pitch of 2 cells of the CCD, but does
not need to be very much greater. The figure of 50 .mu.m for the mask
pattern wavelength compared with 10 .mu.m for the CCD element pitch, so
that one is five times the other, is suitable in practice.
FIG. 6 shows one possible construction for the detector assembly of the
photodetector array 11 and the masks 23, 25 in the embodiment of FIGS. 4
and 5. In FIG. 6 first and second light transmissive elements 27, 29 and
the photodetector array 11 are supported and held rigidly in position by
rigid side pieces 31. The transmissivity patterns forming the masks 23, 25
are formed on the surfaces of the respective light transmissive elements
27, 29, and the side pieces 31 hold the two masks 23, 25 apart from the
distance d.sub.1.
Some difficulty may arise with the construction of FIG. 6, owing to the
need for very good mechanical stability in the detection assembly. With a
CCD having 4096 cells at a 10 .mu.m pitch, the masks being separated by a
distance d.sub.1 of about 5 mm and the wavelength of the mask pattern
being about 50 .mu.m, movements of the order of 10 nm in the pattern of
one of the masks 23, 25 relative to the other can be detected by the
method described above of determining the phase of components in the CCD
output by performing a Fourier transform. Accordingly, the positioning of
the two masks 23, 25 relative to each other in the longitudinal direction
of the masks 23, 25 and the photodetector array 11 must be stable and
non-varying to within a significantly smaller distance than this,
preferably to within less than 1 nm. This is because the system cannot
distinguish between changes in the angle of the light and relative
movement between the two masks 23, 25. Such a very high degree of
mechanical stability can be difficult to obtain with the arrangement of
FIG. 6.
An alternative construction for the detector assembly is shown in FIG. 7.
In this construction, a single light transmissive element 33 is provided,
and the masks 23, 25 are provided by modifying the light transmissivity of
respective opposed surfaces of the single light transmissive element 33.
Accordingly, the distance d.sub.1 between the two masks 23, 25 is defined
by the thickness of the single light transmissive element 33. The side
pieces 31 act to hold the single light transmissive element 33 to the
photodetector array 11.
The construction of the detector assembly can be further simplified and the
physical stability of the assembly can be conveniently provided by the
arrangement shown in FIG. 8, in which the photodetector array 11 is bonded
directly to the single light transmissive element 33 or alternatively is
formed directly on the single light transmissive element 33 as a
substrate. The single light transmissive element 33 can be glass or any
other transparent material suitable for use as a substrate in the process
for forming the photodetector array 11.
In order to provide both of the masks 23, 25 using the detector assembly of
FIG. 8, the second mask 25 may be provided on the surface of the single
light transmissive element 33 on which the photodetector array 11 is
provided. However, this may lead to complications in manufacture, and in
particular it may be difficult to provide the second mask 25 if the
photodetector array 11 is to be formed directly on the single light
transmissive element 33 as a substrate. Accordingly, the detector assembly
of FIG. 8 is more conveniently used in an embodiment of the present
invention having only one variable transmissivity mask 23, which can be
formed on the surface of the light transmissive element 33 remote from the
photodetector array 11.
FIGS. 9 and 10 illustrate a third embodiment of the present invention, in
which only one variable light transmissivity mask is used.
The arrangement of FIGS. 9 and 10 is the same as the arrangement of FIGS. 4
and 5 except that only one mask 23 is present. Accordingly, the pattern of
light and dark formed on the photodetector array 11 is the same repeating
pattern as the pattern of the mask 23. As can be seen from FIG. 10, the
position at which the shadow of any particular point on the mask 23
appears on the photodetector array 11 depends on the angle of the light
reflected from the external measurement mirror 13. Accordingly the phase,
with respect to the photodetector array 11, of the pattern of light and
dark formed on the photodetector array 11 will vary with the angle of the
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