Fringe pattern phase detection system

Electro-optical apparatus measures the average relative phase of an incident wave fringe pattern. The subject fringe, e.g., an interferometric pattern, passes through three sections of an optical mask, one characterized by fixed transmissivity and the other two by quadrature-displaced spatial fringe patterns. The light passing through each section is separately collected and detected to average the respective incident wave/mask section interactions. The phase of the incident fringe pattern relative to the mask is then determined by arithmetically processing the detected signals. In accordance with one aspect of the present invention, the subject fringe pattern is time modulated and the quadrature-shifted mask signals A-C coupled to obviate the requirement for the third, fixed transmissivity mask section.

This invention relates generally to data processing systems and, more 
specifically, to a digital electro-optical system which detects the phase 
of incident fringe patterns. 
BACKGROUND AND OBJECTS OF THE INVENTION 
Important applications of current interest require that the relative phase 
of an incident fringe pattern vis-a-vis a fixed reference be determined. 
Such fringe patterns are developed, for example, by interference between 
split components of a coherent light beam and are used for purposes per se 
well known, e.g., to measure small distance displacements, surface 
contours or irregularities, object shapes and forms, and the like. 
It is an object of the present invention to provide an improved 
electro-optical processing apparatus. 
More specifically, it is an object of the present invention to provide an 
electro-optical system for measuring the phase or phase shift of a wave 
fringe pattern. 
It is another object of the present invention to provide electro-optical 
fringe phase detection apparatus which averages a phase measurement over 
plural cycles (wavelengths). 
Yet another object of the present invention is the provision of fringe 
pattern phase measurement structure operable on a time variable basis to 
obviate processing of bias or direct current signal constituents. 
A still further object of the present invention is to provide 
electro-optical apparatus for effecting complex multiplication. 
SUMMARY OF THE INVENTION 
The above and other objects of the present invention are realized in 
specific, illustrative, electro-optical apparatus which measures the 
average relative phase of an incident wave fringe pattern. The subject 
fringe, e.g., an interferometric pattern, passes through three sections of 
an optical mask, one characterized by fixed transmissivity and the other 
two by quadrature-displaced spatial fringe patterns. The light passing 
through each section is separately collected and detected to average the 
respective incident wave/mask section interactions. The phase of the 
incident fringe pattern relative to the mask is then determined by 
arithmetically processing the detected signals. 
In accordance with one aspect of the present invention, the subject fringe 
pattern is time modulated and the quadrature-shifted mask signals A-C 
coupled to obviate the requirement for the third, fixed transmissivity 
mask section. Pursuant to a further aspect of the instant invention, a 
fringe pattern may be made dependent upon the magnitude and phases of two 
complex numbers to permit complex multiplication.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
Referring now to FIG. 1, there is schematically shown apparatus for 
determining the phase of an incident fringe pattern 10, e.g., in the z 
direction impinging upon the left face of a mask 12. The fringe pattern 10 
is shown as being one dimensional, i.e., as varying in the x direction 
only, where the FIG. 1 apparatus is utilized to determine the relative 
phase of the pattern 10 in that x direction. The fringe pattern 10 may be 
generated in any manner well known to those skilled in the art. Thus, for 
example, the fringe may be an interferometric pattern generated by an 
interference developed when the portions of a split coherent beam undergo 
different physical paths. The optical pattern on mask 12 is illustrated in 
FIG. 2 and is discussed in greater detail below. Suffice it for present 
purposes that the mask 12 has three sections, the upper of which 12.sub.I 
represents an in-phase (i.e., 0-reference phase) component, the middle 
section 12.sub.O comprising a zone of constant light transmissivity, and 
the lower section 12.sub.Q of which is deemed the quadrature-displaced 
section. 
Light from the incident fringe pattern 10 passing through the respective 
sections 12.sub.I, 12.sub.O and 12.sub.Q of mask 12 is focused by a 
cylindrical averaging lens 10 onto one of three light detectors 17.sub.I, 
17.sub.O or 17.sub.Q respectively. The detector outputs are supplied to a 
signal processing circuit 22 described hereinbelow which provides an 
output signal to output utilization means 30. The output signal of circuit 
22 characterizes the relative phase or phase displacement of the fringe 
pattern 10 relative to the quadrature-displaced sections 12.sub.I and 
12.sub.Q of the mask 12. 
Turning now to FIG. 2, there is shown the optical pattern for each of the 
zones 12.sub.I, 12.sub.O and 12.sub.Q of mask 12. The pattern may be 
formed in any manner well known to those skilled in the art, e.g., by 
photodeposition. The in-phase upper section 12.sub.I of mask 12 comprises 
a series of optically opaque areas 13.sub.I having intermediate clear, 
light transmitting areas 14.sub.I therebetween. The alternating areas 13 
and 14 are shown of equal width (50% duty cycle) for purposes of 
illustration only. The relative sizes of adjacent areas 13 and 14 may be 
varied as desired subject only to the constraint that their combined width 
be equal to one wavelength of the fringe pattern, i.e., the distance 
between adjacent lines in the incident fringe field 10. 
The lower, quadrature mask section 12.sub.Q is of substantially the same 
form of the upper mask section 12.sub.I, i.e., contains alternating opaque 
and transparent sections 13.sub.Q and 14.sub.Q with the combined widths of 
contiguous opaque and transparent sections being equal to one wavelength 
at the incident fringe pattern wave frequency. The optical pattern in the 
quadrature shifted section 12.sub.Q is displaced by 90 electrical degrees 
with respect to the upper section 12.sub.I. That is, for example, as 
illustratively shown in FIG. 2, the lower, quadrature section leads the 
pattern in the in-phase section 12.sub.I by one quarter wavelength such 
that the leading edge of each opaque section 13.sub.I begins in the middle 
of the corresponding opaque section 13.sub.Q in the lower section 12.sub.Q 
(for the assumed 50% duty cycle configuration). The purpose of the 
quadrature displacement is discussed hereinbelow. In FIG. 2, the right 
edge of the mask 12 is shown truncated. The mask 12 is made sufficiently 
wide to include a large number of fringe pattern wavelengths such that 
optical averaging occurs over a large number of wavelengths. 
Finally, the central section 12.sub.O of mask 12 includes an area of fixed 
transmissivity. For purposes below discussed, the transmission properties 
of the central section 12.sub.0 is made to be one-half of the value 
between the clear and dark sections 14 and 13 of the mask sections 
12.sub.I and 12.sub.Q. Alternatively, the mask section 12.sub.O may be 
made clear, and a suitable electrical one-half correction made via an 
attenuator following the light detector 17.sub.O below discussed. 
With the above configuration in mind, attention will now be returned to 
FIG. 1. The apparatus there shown determines the relative phase or phase 
displacement of the incident fringe pattern 10. Let the transmittance of 
the mask 12 sections 12.sub.I, 12.sub.O and 12.sub.Q be represented by 
T.sub.I, T.sub.O and T.sub.Q, where 
EQU T.sub.I =1/2 (1+cos kx) (1) 
EQU T.sub.O =1/2 (2) 
EQU T.sub.Q =1/2 (1-sin kx) (3) 
The incident spatial fringe pattern 10 is described by 
EQU I(x)=A+B(x) cos(kx+.phi.) (4) 
where A is the D-C bias intensity, B(x) is the fringe spatial modulation, 
if any, in the x direction; and .phi. is the fringe phase shift relative 
to the mask 12 which is to be determined. 
The amount of light passing through the upper or in-phase section 12.sub.I 
of mask 12 is the product of the light intensity I(x) incident and the 
transmissivity function T.sub.I of the mask portion 12.sub.I : 
EQU I.sub.I =I(x).multidot.T.sub.I =1/2(A+B(x).multidot.cos(kx+.phi.)) +1/2(A 
cos(kx)+B(x).multidot.cos(kx+.phi.).multidot.cos kx) (5) 
As earlier observed, the cylindrical lens 15 performs an integration or 
averaging function over the width of the mask 12 since all rays, wherever 
occurring, algebraically add when focused upon the light detector 17. 
Accordingly, all terms in the equation 5 representation of the light 
I.sub.I reaching detector 17.sub.I which include a term cos kx (or any 
other sinusoidal function of x) go to zero, the integral of the cosine 
over many wavelengths being substantially zero. Accordingly, Equation 5 
reduces to 
EQU I.sub.I =1/2A+1/2B(x).multidot.cos(kx+.phi.).multidot.cos kx (6) 
Using the identity 
EQU cos A.multidot.cos B=1/2cos (A+B)+1/2cos (A-B), (7) 
The light I.sub.I reaching detector 17.sub.I is given by 
EQU I.sub.I =1/2A+1/4B(x).multidot.cos(2kx+.phi.)+1/4B(x).multidot.cos.phi.(8) 
The middle term in Equation 8 being a function of cos(2kx+.phi.), this term 
goes to zero for the reason above discussed. Accordingly, the light 
incident detector 17.sub.I is given by 
EQU I.sub.I =1/2A+1/4B cos .phi., (9) 
where B is the average of B(x) over the width of the mask. In many cases, 
B(x) will simply be a constant in any event even before averaging. 
The light I.sub.0 passing through the middle portion 12.sub.0 of mask 12 
and reaching the light detector 17.sub.0 via the collecting lens 15 is 
given by the product of the incident light I(x) and the transmissivity 
T.sub.0 of the middle portion, such that 
EQU I.sub.0 =1/2A+1/2B(x)cos(kx+.phi.) (10) 
Since the second term in Equation 10 includes as a factor a cosine with an 
x-dependent argument, this term approaches zero and thus 
EQU I.sub.0 =1/2A. (11) 
The light I.sub.Q reaching the light detector 17.sub.Q via the mask lower 
portion 12.sub.Q is the product of the incident light I(x) and the mask 12 
quadrature section transmissivity T.sub.Q. By an analysis identically 
paralleling that given above for the upper mask portion 12.sub.I in 
Equations 5-9, 
EQU I.sub.Q =I(x).multidot.T.sub.Q =1/2A+1/4B sin .phi.. (12) 
As above noted, it is the ultimate objective of the FIG. 1 system to 
determine a value for the displacement angle .phi., i.e., the amount in 
which the incident fringe pattern 10 phase differs from the in-phase or 
reference phase mask component 12.sub.I. To this end, it is observed that 
EQU .phi.=tan.sup.-1 (I.sub.Q -I.sub.O)/(I.sub.I -I.sub.O) (13) 
since, by inserting the relationships for I.sub.Q (Eq. 12), I.sub.0 (Eq. 
11) and I.sub.I (Eq. 9) into Equation 13, 
EQU .phi.=tan.sup.-1 (B/4 cos.phi.)/B/4 sin .phi.)=tan.sup.-1 (sin .phi./cos 
.phi.) (14) 
For small angles where 
EQU .phi..apprch.tan .phi., (15) 
the approximation for 0 is 
EQU .phi..apprch.(I.sub.Q -I.sub.0)/(I.sub.I -I.sub.0). (16) 
As above noted the light detector array 17 includes elements 17.sub.I, 
17.sub.O and 17.sub.Q for respectively providing an electrical output 
signal proportional to the light I.sub.I, I.sub.0 and I.sub.Q incident 
thereon representing the component of the incident fringe pattern 10 which 
passes through the corresponding mask section 12.sub.I, 12.sub.0 and 
12.sub.Q via the averaging lens 15. Each detector 17 may comprise any 
device well known to those skilled in the art for converting a light 
amplitude into an electronic voltage amplitude, e.g., photomultipliers, 
photodiodes, or the like. Thus, the electrical output signals from the 
detector array 17.sub.I, 17.sub.0 and 17.sub.Q provide a measure of the 
quantities I.sub.I, I.sub.0 and I.sub.Q of Equations 9, 11 and 12, 
respectively. 
In the signal processing circuit 22, an algebraic summing (here 
subtracting) element 26 (e.g., an operational amplifier with non-inverting 
and inverting inputs) generates the quantity I.sub.Q -I.sub.0 in the arc 
tangent numerator of Equation 13 by subtracting 1/2A (Equation 11) from 
the I.sub.Q relationship of Equation 12. Similarly, an algebraic summing 
(arithmetically subtracting) element 23 develops the arc tangent 
denominator I.sub.I -I.sub.0 of Equation 13 by subtracting 1/2A (Equation 
11) from I.sub.I (Equation 9). The quotient (I.sub.Q -I.sub.0)/(I.sub.I 
-I.sub.0) is then computed in a divider circuit 28 and may directly 
constitute a measure of the phase .phi. to be measured if small angle 
displacement is assumed (Equation 16). If larger angle displacements are 
permissible or contemplated in the application of the FIG. 1 system, 
output utilization means 30 (or signal processing circuit 22) includes 
apparatus for computing the arc tangent function of the argument supplied 
thereto by the divider 28 (Equation 13) to develop a more precise value 
for the phase angle .phi.. In either event, output utilization means is 
furnished with the phase angle .phi. for differing uses depending upon the 
specific application intended. Thus, for example, where distance is 
measured by interferometric interference, the phase angle .phi. represents 
distance and can be used in a servomechanism controller to reposition a 
controlled element as desired. This type of application is useful as in 
robotics to control the relative position of a robotic work element (e.g., 
welder, grasping arm or the like) vis-a-vis a work piece to be operated 
upon. 
The signal processing circuit 22 is shown as implemented by discrete 
algebraical adder and divider elements 23, 26 and 28 which may be analog 
in nature. The signal processing circuitry 22 (and the arc tangent 
calculation of output utilization means 30 if desired) may of course all 
be implemented by a single microprocessor where the electrical 
representations of the light quantities I.sub.I, I.sub.0 and I.sub.Q 
become microprocessor input variables entered as via a multiplexer and 
analog-to-digital converter. 
The above arrangement has thus been shown to compute the relative phase of 
a one dimensional fringe pattern 10 relative to the reference phase 
defined by the upper section 12.sub.I of a mask 12. 
Turning now to FIG. 3, there is shown an interferometer application of the 
instant invention. A coherent light beam 50 is incident upon a beam 
splitting mirror 51. A portion of the incident beam reflected by mirror 51 
follows a solid line path in FIG. 3 beginning with path portion 52 to the 
lower fully reflecting surface of a mirror 52. This reflected beam follows 
the path 54 passing through the mirror 51 and is incident upon the mask 12 
via the path 55. A second portion of the light beam 50 incident the beam 
splitting mirror 51 follows the dotted path, passing through the mirror 51 
and following the dotted path 57 to a second fully reflecting mirror 54, a 
mirror 54 reflected path leg 60, and a mirror 51 reflected path portion 62 
to the mask 12. 
The two coherent beam signals reaching the mask 12 via path legs 55 and 62 
interfere and cause a fringe pattern 10 on the face of the mask 12 of the 
composite FIG. 1 apparatus. If any small displacement occurs for the 
mirror 54 relative to the mirror 52, the interference pattern will change 
its phase and this phase change will be detected by the FIG. 1 apparatus. 
Thus, the output of divider circuit 28 coacting with the utilization means 
30 may be employed as an error detector in a servomechanism loop to 
maintain the relative distance between mirror surfaces 52 and 54 in any 
relationship desired to an accuracy a small fraction of the wavelength of 
the coherent light of beam 50. Obviously, one reflecting surface 52 or 54 
may be fixed, and the other disposed on any mechanical element whose 
position is to be monitored or controlled. 
The interferometer application above discussed and shown in FIG. 3 is for 
purposes of illustration only. For example, the fringe pattern 10 may vary 
in two directions (x and y shown in FIG. 1). A beam splitting mirror 
(comparable to the mirror 51 in FIG. 3) may be disposed to the left of the 
mask 12 in FIG. 1. The FIG. 1 apparatus will then operate in the manner 
fully set forth above to detect the phase displacement .phi. in the x 
direction. The FIG. 1 apparatus is also replicated in a vertical 
orientation (but rotated 90.degree.) to detect the phase variation in the 
y direction of the incident two dimensional fringe pattern furnished by 
the beam splitting mirror. 
Moreover, the instant invention is not limited to Cartesian fringe fields. 
Coherent light applications (e.g., lasers with end mirrors) generate an 
etalon fringe formed of concentric circles. The in-phase and quadrature 
mask components for such a fringe field formed of concentric circles would 
themselves thus be concentric circles spatially radially displaced by 
90.degree.. Similarly, any incident fringe field of whatever shape may be 
phase detected by having in-phase and quadrature masks or mask sections, 
again offset by 90 degrees (one-quarter of the inter-line spacing). 
It is observed that the central mask section 12.sub.0 was required to 
generate the quantity 1/2A (Equation 11) for purposes of the algebraic 
subtractions of Equation 13 and/or 15. In physical terms, this subtracts 
out a fixed, time-invariant bias term. If the quantities B/4 cos .phi. 
(Equation 9) and B/4 sin .phi. (Equation 12) can be made time dependent, 
the undesired A 1/2 bias term can be eliminated by high pass filtering. 
This may be effected, for example, by electronically controlling 
(modulating) the light passage portions 14 of mask sections 12.sub.I and 
12.sub.Q (e.g., by making the clear portions 14 of electronically 
sensitive liquid crystals such that the portions are either opaque or 
transparent depending upon the applied potential). Once a time dependency 
is imparted, as above noted, the outputs of the light detectors 17.sub.I 
and 17.sub.Q are simply A-C (capacitively) coupled to the divider circuit 
28 input terminals. 
Turning now to FIG. 4, there is shown apparatus for generating a fringe 
pattern (output of Bragg cell 82) which permits complex multiplication 
after processing by the FIG. 1 apparatus. Applications of present 
importance require that two complex quantities be multiplied as in radar 
signal processing and radar signal jamming and noise avoidance, ultrasound 
signal processing to avoid spurious noise signals and so forth. In such 
applications a first complex number may be given by A.sub.1 e.sup.i.phi. 1 
and a second complex number given by A.sub.2 e.sup.i.phi. 2. Such complex 
numbers are supplied in FIG. 4 via the sources thereof 65 and 68. A 
carrier source 70 is applied to two amplitude modulators 75 and 78 the 
outputs of which are thus A.sub.1 cos(.omega.t+.phi..sub.1) and A.sub.2 
cos(.omega.t+.phi..sub.2). The first complex number at the .omega. carrier 
frequency is employed to modulate the amplitude of light supplied by a 
light source 80 which is used to strobe the Bragg cell 82. A lens may be 
employed intermediate light source 80 and Bragg cell 82 such that the 
entire width of the Bragg cell may be illuminated with a plane wave. The 
second signal representing a complex quantity at carrier frequency 
supplied by modulator 78 modulates the ultrasonic transducer in the Bragg 
cell. 
As is per se well known, the ultrasonic transducer in a Bragg cell gives 
rise to alternating area of local compaction and rarification in the Bragg 
cell glass as the ultrasonic wave propagates therethrough, thus creating 
areas of increased and decreased index of refraction in the glass. Thus, 
when the light supplied by the source 80 passes through the Bragg cell, 
since it is of the same frequency as the excitation applied to the 
transducer (coherent signals), the output of the Bragg cell is in all 
material respects a fringe pattern. Since light source 80 acts as a strobe 
for the traveling acoustic wave through the Bragg cell glass, the areas of 
perceived light peaks and troughs shift spatially as the phase varies 
between complex numbers. Similarly, the amount of light exciting the Bragg 
cell is proportional to the product of the light supplied by source 80 
(applied excitation) and the applied acoustic modulation (degree of index 
of refraction modulator). 
In complex multiplication, it is desired to determine the quantity A.sub.1 
.multidot.A.sub.2 which is the amplitude of the multiplied complex numbers 
ad to obtain a measure of the sum of the complex phase angles, i.e., 
(.phi..sub.1 +.phi..sub.2). That is, the amplitude product and the phase 
angle sum provide the results of the complex multiplication. When the 
fringe pattern of FIG. 4 is applied to the FIG. 1 electro-optical system, 
the summed phase angle information is identically present at the output of 
the FIG. 1 divider circuit 28 (small angle assumption) or the arc tangent 
computation in output utilization means 30. Similarly, the amplitude 
product A.sub.1 A.sub.2 is available at the output of the light detector 
17.sub.0 with a scaling factor of "2" which can be supplied by an 
operational amplifier or otherwise in a manner well known to those skilled 
in the art. Accordingly, the fringe pattern developed in accordance with 
FIG. 4, impinging upon the FIG. 1 system, provides a fast, inexpensive way 
of rapidly effecting complex multiplication. 
The above-described apparatus is merely illustrative of the principles of 
the present invention. Numerous modifications and adaptations thereof will 
be readily apparent to those skilled in the art without departing from the 
spirit and scope of the present invention.