Position detector and method of measuring position

According to the principles of the invention, an improved system and method of accurately measuring the position of an object to high resolution are provided. A read head is positioned adjacent a grating. The read head emits light onto the grating. The light is diffracted into two light beams by the grating. The light beams are reflected back towards the grating, to be diffracted a second time and combined into a single beam. The polarization of the respective light beams is modified before being diffracted the second time. The polarization component of the beam parallel to the diffraction grating grooves is rotated perpendicular to the diffraction grating grooves and the component of the beam perpendicular to the diffraction grating grooves to be rotated parallel to the diffraction grating grooves. The effects of the diffraction on perpendicular or parallel polarized light are canceled because the same light impinges at two different polarizations, each the opposite of the other, prior to being combined into a single beam.

DESCRIPTION 
1. Technical Field 
This invention relates to position detectors using a diffraction grating to 
sense displacement, and more particularly, to a method and system for 
increasing the accuracy and resolution in such a position detector. 
2. Background of the Invention 
One prior art system for sensing the position of an object to an accuracy 
below the micrometer range utilizes laser diode light diffracted from a 
reflective diffraction grating. Light impinging on the grating is 
diffracted and reflected into two diffraction beams. Each diffracted beam 
is reflected back to the grating, diffracted a second time, and combined 
into a single beam. The beams are polarized at right angles to each other 
before the second diffraction to prevent them from interfering in the 
combined beam. The average intensity of the combined signal is sensed in a 
photodetector, providing a DC level component. The combined beam then 
passes through a polarizer which selects components of each beam for 
interfering with each other. 
The phase difference between the two beams is based on the position of the 
diffraction grating, so that as the diffraction grating moves, the phase 
relationship of the two beams changes, causing them to constructively or 
destructively interfere. For first order diffractions, the peak-to-peak 
period of the interfering beams is p/4, where p is the pitch of the 
diffraction grating. Thus, for diffraction gratings having a pitch of 1 
micron, a peak in the interfering beams occurs each time the scale moves 
1/4 of a micron, or 250 nm. 
Scale position within 250 nm can be measured with some accuracy by sensing 
the peaks of the output signal as the scale is laterally displaced. For 
measuring scale position more accurate than 250 nm, scale displacement 
between peaks must be estimated by interpolations. Presently, the prior 
art attempts to establish a position to within 10 nm, but is not able to 
measure any position with more accuracy than this. Further, because of 
numerous possible problems in the prior art devices, as will be explained 
herein, true accuracy may not be within 10 nm, but the user is not aware 
of the position being inaccurate. If the user wishes to ensure accurate 
measurements within 10 nm, a laser interferometer is required. The laser 
interferometer is much more expensive, complex, and delicate than a diode 
light source diffraction grating. A diode-based position detector which 
accurately measures a position to within 10 nm or less would be useful to 
replace current expensive systems requiring the use of a laser 
interferometer. 
SUMMARY OF THE INVENTION 
According to the principles of the invention, an improved system and method 
of accurately measuring the position of an object to high resolution are 
provided. A read head is positioned adjacent to a grating. The read head 
emits light onto the grating. The light is diffracted into two light beams 
by the grating. The light beams are reflected back towards the grating, to 
be diffracted a second time and combined into a single beam. The 
polarization of the respective light beams is modified before being 
diffracted the second time. The polarization component of the beam 
parallel to the diffraction grating grooves is rotated perpendicular to 
the diffraction grating grooves and the component of the beam 
perpendicular to the diffraction grating grooves is rotated parallel to 
the diffraction grating grooves. The effects of the different diffraction 
efficiencies of perpendicular and parallel polarized light, respectively, 
are canceled because the same light impinges at two different 
polarizations, each the opposite of the other, prior to being combined 
into a single beam. 
In one embodiment, polarizers screen out light in a selected polarization 
angle so that the beam is polarized either perpendicular or parallel to 
the grating grooves. For this embodiment, the polarization of the beams 
exiting the polarizers is rotated by 90.degree., to reverse the 
polarization direction, making the parallel polarized beam perpendicular 
and the perpendicular polarized beam parallel to the grating grooves. 
In another embodiment, the reflected light does not pass through 
polarizers, and the beams pass through polarization mirroring stages to 
mirror their polarization about a selected axis. In this embodiment, one 
of the beams is mirrored about the perpendicular component to reverse the 
direction of the parallel component and then mirrored 45.degree. to the 
perpendicular to provide a wave having the parallel and perpendicular 
components switched. The other beam is mirrored 45.degree. to the parallel 
to provide the polarized, rotated light beam. 
The location at which the reflected light beams strike the diffraction 
plate relative to the first light beam is selected to provide a longer 
scale run in one embodiment. For example, the two locations of light 
impinging upon the diffraction grating are aligned perpendicular to the 
direction of travel of the grating so that the sensing pattern takes up 
less area and the same length of scale can be used to measure greater 
displacements. 
In a further alternative embodiment, the light impinges upon the 
diffraction grating at an acute angle to the surface to enable reading 
scales with a smaller grating pitch than possible in the prior art. The 
angle is preferably the same as the positive diffraction angle. 
The diffraction grating may be a simple grating having all grating grooves 
parallel to each other and perpendicular to the direction of movement to 
provide position sensing along a single axis. Alternatively, the grating 
may be an X-Y grid to permit position sensing in the X and Y axes. The 
grating can be either a transmissive grating or a reflective grating. 
This invention thus provides the advantage that linear displacements and 
exact positions can be accurately measured to better than 10 nm using a 
relatively inexpensive light source and grating because, according to the 
invention, the polarizing effects of the scale grating are neutralized. A 
second advantage over the prior art is that the intensity of the light at 
a second reflection from a diffraction grating is significantly greater 
than such a reflection in a prior art device, thus providing a device 
which is also less susceptible to noise. Having the incident beam from the 
light source at an angle with respect to the diffraction grating permits 
use of a diffraction grating having a pitch which is shorter than the 
wavelength of the light, an advantage not possible with the prior art 
device. Further advantages to having the incident beam from the light 
source at an angle with respect to the diffraction grating are that 
back-reflected light into the input beam is avoided and harmful effects of 
multiple reflections within the read head are eliminated.

DETAILED DESCRIPTION OF THE INVENTION 
FIG. 1 illustrates a position detector according to the prior art, as 
illustrated in laid open Japanese patent publication no. 1-26005. In the 
prior art position detector, a monochromatic light source 10, such as a 
laser diode, together with a collimator 12, projects a collimated beam to 
a mirror 14 and upon a diffraction grating scale 16, normal to the surface 
of the scale. The light is diffracted by the diffraction grating 16 into 
positive and negative orders 17 and 18. The beams are diffracted at an 
angle of .theta. and -.theta., respectively, with respect to the normal to 
the surface. 
FIG. 2a is an enlarged side view of the diffraction grating scale 16 of 
FIG. 1 illustrating the diffraction of the first order light beams. The 
diffraction member 16 is coupled to an object 23 which undergoes lateral 
displacement along the direction indicated by arrow 22, the movement being 
perpendicular to the individual grating grooves 20. Light beam 15 impinges 
on the diffraction grating 16 normal to the surface. The positive angle 
diffraction beam 17 is diffracted from the grating at an angle .theta., 
relative to the surface normal of the diffraction grating 16. The negative 
angle diffraction beam 18 is diffracted from the grating 16 at an angle 
-.theta., having an equal value to .theta., but opposite in sign. 
As illustrated in FIG. 2b, the diffraction grating grooves 20 extend 
parallel to each other. The pitch p of one diffraction grating groove 20 
is from a point on one grating groove 20 to the same point on an adjacent 
grating groove 20. The pitch p in a diffraction grating according to the 
prior art might be in the range of 1.6 to 1.0 microns, one micron being 
10.sup.-6 m. The width of the beams 15, 17, and 18 is generally in the 
range of several millimeters, and thus the beams will generally cover many 
thousands of the individual grating grooves 20. 
The position of the diffraction grating scale 16, and thus of an object 23 
coupled to the scale 16, is determined in the prior art system of FIG. 1 
as follows. The light beam 15 first strikes the surface at point 13, and 
is diffracted into two beams, as just explained. The positive angle 
diffraction beam 17 is reflected by retro-reflector 25 back to the surface 
at a selected point 24 to impinge upon the diffraction grating scale 16. 
Similarly, the negative angle beam 18 is reflected by retro-reflector 27 
to impinge upon the same spot 24 of the diffraction grating scale 16. 
Prior to the diffraction beams 17 and 18 striking the diffraction grating 
scale 16 a second time, the beams pass through respective linear 
polarizers 26 and 28, which screen the light so that it is polarized in a 
selected plane. The polarizers 26 and 28 are oriented with their 
polarization axes perpendicular to each other so that the resultant 
respective beams 30 and 32 are polarized at right angles to each other. 
The beams strike at the same point 24 on the scale, and, upon being 
diffracted a second time, form a combined beam 34. 
It is well known that two rays polarized at right angles to each other do 
not interfere when combined into a single beam. Even though the combined 
beam 34 is a combination of two beams of the same wavelength, they are not 
interfering with each other because their polarizations are at right 
angles. The beam 34 is sensed by photodetector system 11 in the following 
manner. 
As shown in FIG. 2c, the beam 34 enters a photodetector system 11 having 
various beam splitters and photodetectors. A beam splitter 36 diverts a 
portion of the output beam 34 to photodetector 38, which detects the 
average intensity of the combined output beam 34. Beam splitter 40 splits 
the beam 34 into two components 42 and 44. One of the components, 44, 
passes through a .lambda./4 delay plate 46 and then passes through a 
polarizer 48, after which its intensity is detected by photodetector 50. 
The other portion of the beam 42 passes through polarizer 52 and its 
intensity is sensed by photodetector 54. The respective polarizers 48 and 
52 are oriented at the same angle, generally at 45.degree. from the 
polarization angle of each of the two portions of the combined beam 34. 
The output of each of the polarizers 48 and 52 is a combined beam having 
the two components of the diffracted beams polarized in the same plane. 
The two rays 30 and 32 do not interfere while at right angles, but do 
interfere when brought into the same plane of polarization. The respective 
polarizers 48 and 52 thus cause the components of the beam 34 to interfere 
with each other. The interfering beams may constructively interfere or 
destructively interfere, depending on the relative phase of the beams. As 
is known in the prior 15 art, the relative phase difference between the 
positive angle diffraction beam 17 and the negative angle diffraction beam 
18 varies with the position of the diffraction grating 16. The phase 
difference P is related to the amount of scale displacement x according to 
the following equation: 
EQU P=4*n (x/p)*(2*.pi.) (1) 
where n is the order of diffraction, p is the scale pitch, P is the 
relative phase difference of the two beams, and x is the displacement of 
the scale. 
As illustrated in FIG. 3a, the intensity of the light beam 53 varies 
according to a sine wave pattern with displacement of the diffraction 
scale 16 along the X axis as the relative phase of the two beams causes 
either destructive or constructive interference For constructive 
interference, the intensity of the light beam has a maxima at 51, and for 
destructive interference, it has a minima at 55. For first-order 
diffractions (n=1) the period of the sine wave is p/4, as illustrated in 
FIG. 3a. Similarly, the signal 49 varies as the diffraction grating scale 
16 is displaced. The light intensities of waves 49 and 53 offset at 
90.degree. with respect to each other because the .lambda./4 delay plate 
46 delays light beam 49 to place it 90.degree. lagging behind wave 53, 
which produces two quadrature signals for providing an indication of the 
direction of movement of the diffraction member 16. The intensity of the 
quadrature signals 53 (I.sub.1) and 49 (I.sub.2) is given by the following 
equations: 
EQU I.sub.1 =DC+A * cos(P) (2) 
and 
EQU I.sub.2 =DC+A * sin(P) (3) 
where I.sub.1 and I.sub.2 is the respective intensity of signals 53 and 49, 
DC is the average intensity level, A is the amplitude of the sinusoidal AC 
component, and P is the phase difference between the two component beams A 
third signal, I.sub.3 is also obtained from detector 38, which is 
proportional to the average intensity level according to the equation: 
EQU I.sub.3 =K*DC (4) 
where DC is the average intensity level and K is a constant factor. The 
photodetector 38 senses the average intensity prior to the polarization of 
the two waves being aligned by polarizers 48 and 52 and thus is (in the 
ideal case) the average intensity of the two component beams when they are 
not interfering. 
The light beams 49, 53, and 34 are converted to electrical signals by 
respective photodetectors 50, 54, and 38 as described, amplified and fed 
to a counter which computes and displays the scale displacement x in a 
manner well known in the prior art. The system of FIGS. 1-3a as just 
described is based on known prior art devices. However, these systems have 
significant problems in providing accurate measurements of displacements 
less than 0.25 microns, for reasons which will now be described. 
In order to obtain higher accuracy than the period of the output signals 
I.sub.1 and I.sub.2, one has to estimate the phase P within the period by 
use of interpolation. For achieving best interpolation accuracy the 
amplitude, A, of the quadrature signals should be kept constant. This can 
be done by requiring that the scale must have the same diffraction 
efficiency over the scale area, but this is difficult to achieve. 
A more feasible way of dealing with this problem is to apply an automatic 
gain control to the quadrature signals by sensing the amplitude A, and 
adjust either the source output power or the signal amplitude at the 
output amplifiers so that A is kept constant. However, the problem is to 
sense the amplitude A. 
Prior art (e.g., U.S. Pat. No. 4,629,886) uses the method of squaring the 
signals I.sub.1 and I.sub.2 (after subtracting the average signal level 
DC, available from signal I.sub.3), adding the squared signals together, 
and taking the square root of the sum, thereby obtaining the amplitude A. 
However, this is a method which requires complex and expensive analogue 
circuitry. 
Prior art (e.g., U.S. Pat. No. 4,629,886) also uses signal I.sub.3, 
proportional to the average signal level DC, as a measure of the amplitude 
A. Due to the polarization effect of the scale, this technique does not 
provide an accurate measurement. 
Prior art (e.g., U.S. Pat. No. 4,676,645 and Japanese laid open application 
no. 62-200219) discloses a device using two separate beams striking the 
scale. One disadvantage of the two beam systems is that the two beams 
strike the scale at different points and then are recombined to form a 
single beam. If there are any errors or deviations in the scale at one 
point but not another, the result of these differences is magnified rather 
than eliminated, causing an error in the measurement. A further 
disadvantage is that because there are two input beams striking the scale, 
there is a likelihood that their path lengths will not be equal prior to 
and after striking the scale. The system is sensitive to either yaw or 
tilt variations in scale orientation because a beam splitter is used to 
creat two input beams and to combine two beams. Errors will thus occur for 
slight variations in yaw or tilt of the scale. These devices are also 
susceptible to differences in scale variations along its length, grating 
groove spacing, and dimensions at different points along the entire length 
of the scale, a problem specifically solved by the structure of this 
invention, as described herein. The use of a beam splitter to create and 
then recombine the two beams creates the potential for more errors. The 
embodiment of FIG. 8 of the '645 patent still has the problem of two 
separate angles and is thus sensitive to any variations in scale yaw or 
tilt, differences in the angle of incidence, or different path lengths. 
The devices of these two prior art patents thus introduce errors that 
prevent their use as precision measuring devices. 
One shortcoming of the prior art is the assumption that the diffraction 
efficiency of a beam polarized parallel to the individual grating grooves 
20, as shown in FIG. 2b, is identical to the diffraction efficiency of a 
light beam polarized perpendicular to the diffraction grating grooves 20. 
Unfortunately, the ratio between the diffraction efficiencies of a beam 
parallel polarized (p-polarized) or perpendicular polarized (s-polarized) 
usually varies over the diffraction grating scale 16 surface area due to 
imperfections in the manufacture of the grating scale 16. Consequently, 
prior art methods which failed to account for differences in p- and 
s-polarization diffraction efficiencies based on the polarization of the 
light are prone to errors in providing the exact position and accurately 
measuring the displacement as the object moves. Consequently, the prior 
art device shown in FIG. 1 can only be assumed to be accurate to within 10 
nm. If the ratio between the p- and s-polarization diffraction 
efficiencies varies beyond an expected value due to an imperfection in the 
scale, the error may be greater than 10 nm. 
For the prior art device of FIG. 1, assume that the polarization direction 
of the linearly polarized input beam 15 is oriented 45.degree. to the 
grating grooves 20 of the diffraction grating scale 16. The diffraction 
efficiency for the p-polarization is kp and the diffraction efficiency for 
the s-polarization is ks. The diffraction efficiencies denote the 
amplitude efficiencies of the diffracted light with the respective 
parallel and perpendicular polarizations. Assume further that the 
polarizers 26 and 28 are oriented with the polarizer 26 perpendicular to 
the grating grooves and the polarizer 28 parallel to the grating grooves. 
With these assumptions, the following equations define the amplitude of 
the light components in the combined beam 34, after being diffracted by 
the grating a second time at point 24. 
EQU E.sub.lp =B*kp*kp*cos(.omega.t+P/2) (5) 
EQU E.sub.ls =0 (6) 
EQU E.sub.rp =0 (7) 
EQU E.sub.rs =B*ks*ks*cos(.omega.t-P/2) (8) 
E.sub.lp and E.sub.ls are the vector components of the beam 32 after being 
diffracted at 24 E.sub.lp being the parallel polarized component and 
E.sub.ls being the perpendicular polarized component E.sub.rp and E.sub.rs 
are the vector components of the beam 30 after being diffracted at 24, 
E.sub.rp being the parallel component and E.sub.rs being the perpendicular 
component. (E.sub.r refers to the right-hand beam 30 in all the figures, 
for ease in terminology; it is the positive angle diffraction beam. 
Similarly E.sub.l refers to the left-hand beam 32, which is the negative 
angle diffraction beam.) As previously stated, the polarizer 26 filters 
out light parallel to the grating grooves in beam 30, and thus E.sub.rp 
=0. The polarizer 28 filters light perpendicular to the grating grooves, 
and thus E.sub.ls =0 in beam 32. As can be seen from equation 5, the 
diffraction efficiency kp is multiplied by itself and thus the effect is 
squared in that portion of the output beam 34. Similarly, the effect of 
the perpendicular polarization efficiency is squared. 
The output beam consists of the combination of the left- and right-hand 
diffracted beams with their polarization being perpendicular (and thus not 
interfering), which permits us to describe the components of the output 
beam as follows: 
EQU E.sub.op =B*kp.sup.2 *cos(.omega.t+P/2) (9) 
EQU E.sub.os =B*ks.sup.2 *cos(.omega.t-P/2) (10) 
where E.sub.op and E.sub.os are the respective vector components of the 
output beam 34 having p- and s-polarizations. The output beam is then 
passed through polarizer 52 to obtain the first output signal I.sub.1 
which is a combination of the two beams as follows: 
EQU I.sub.1 =C * [kp.sup.4 +ks.sup.4 +2*kp.sup.2 *ks.sup.2 *cos(P)](11) 
where C is another proportionality factor. The component E.sub.op of the 
second output beam 49 is retarded by 90.degree. by letting it pass through 
the .lambda./4 wave delay plate to obtain the second quadrature signal as 
follows: 
EQU I.sub.2 =C [kp.sup.4 +ks.sup.4 +2*kp.sup.2 *ks.sup.2 *sin(P)](12) 
Segmenting I.sub.1 and I.sub.2 into the DC and amplitude components we 
obtain the following: 
EQU DC=C*(kp.sup.4 +ks.sup.4) (13) 
and 
EQU A=2*C*kp.sup.2 *ks.sup.2 (14) 
The DC level of the output beam 34 sensed by photodetector 38 is 
proportional to the sum of the squares of E.sub.op and E.sub.os as given 
by equations 9 and 10 to obtain the following: 
EQU I.sub.3 =D*(kp.sup.4 +ks.sup.4) (15) 
where D is a proportionality factor. The signal I.sub.3 is thus 
proportional to the average intensity DC level at photodetector 38 and can 
be used to measure DC. However, I.sub.3 is not, in general, proportional 
to the amplitude A of equation 14. For I.sub.3 to be proportional to the 
amplitude A, the ratio between the diffraction efficiencies for p- and 
s-polarizations must be constant over the entire diffraction grating scale 
16. This, of course, is generally not the case. Thus equations 1 to 15 
illustrate the problems of a prior device. 
FIG. 4a illustrates a displacement detection system operating according to 
the principles of the invention to overcome the problems of the prior art. 
According to the principles of the invention, a detection circuit is 
provided in which the DC value sensed by photodetector 38 is assured of 
being directly proportional to the amplitude A and thus can always be used 
for controlling the amplitude A with an automatic gain control system. In 
addition, the polarization effect of the scale on the diffracted beams is 
corrected by adjusting the polarization between the first and second times 
the beams strike the diffraction grating 16 to cancel the effects. The 
polarization of the two components of the output beam is rotated such that 
each portion of the beam encounters the same diffraction efficiencies. 
As shown in FIG. 4a, the system for compensating for the polarization 
effects includes .lambda./2 delay plates 60, 62 positioned in the light 
beam diffracted from the point 13 prior to striking the grating scale 16 a 
second time at point 24. (Like elements from the prior art of FIG. 1 have 
the same reference numbers.) As is known in the prior art, a .lambda./2 
delay plate has the property of producing a mirror image about its fast 
axis of the state of polarization of the input beam to the plate. 
(.lambda./2 delay plates per se and their properties are known in the 
prior art, and any known prior art .lambda./2 delay plate is acceptable 
for use in this invention.) The fast axis of the .lambda./2 delay plates 
60 and 62 is oriented 45.degree. with respect to the polarization 
direction of the respective polarizers 26 and 28 to turn the polarization 
direction of the respective output beams 37 and 39 exactly 90.degree.. 
After having turned the polarization direction of each of the beams 
90.degree., the beams strike the grating scale 16 at point 24 and are 
diffracted a second time and combined into a single beam 64. 
The right-hand beam exiting from the polarizer 26 represents that portion 
of the beam 17 which has been affected by the perpendicular diffraction 
efficiencies when first striking the grating scale 16 at point 13. The 
polarization of this beam is then rotated by delay plate 60 so that it is 
attenuated by the parallel diffraction efficiencies when it strikes the 
grating scale 16 a second time as beam 39. Similarly, the left-hand beam 
exiting from the polarizer 28 has been attenuated by the parallel 
diffraction efficiency when first striking the scale at point 13, and is 
rotated to a polarization perpendicular to the diffraction grating grooves 
20 prior to striking the grating 16 a second time at 24 as beam 37. Thus, 
each portion of the beam 64 is attenuated once by the parallel 
polarization diffraction efficiency and once by the perpendicular 
polarization diffraction efficiency. Both beams 37 and 39 pass through the 
same diffraction efficiencies, effectively canceling the relative change 
in intensity based on differences in diffraction efficiency and ensuring 
that the ratio between the two beams based on differences of polarization 
diffraction efficiencies is always equal to 1. 
The equations describing the components of output beam 64 following the 
principals of the invention are as follows: 
EQU E.sub.op =B*ks*kp*cos(.omega.t+P/2) (16) 
EQU E.sub.os =B*kp*ks*cos(.omega.t3`P/2) (17) 
As is clear from equations 16 and 17, the effect of the diffraction 
efficiencies ks and kp are multiplied by each other in both the right-hand 
and left-hand beams. The value of kp*ks will equal the value of ks*kp. The 
difference between the prior art device can readily be seen by comparing 
equation 16 with equation 9. According to equation 9, the parallel 
diffraction efficiency kp is multiplied by itself to create a factor of 
kp.sup.2, which will cause an error if kp.noteq.ks. Similarly, equation 10 
contains a ks.sup.2 factor. However, in both equations 16 and 17, kp is 
multiplied by ks, effectively canceling error rather than squaring it. 
The quadrature output signals according to the device of the present 
invention thus become 
EQU I.sub.1 =C * [(kp.sup.2 *ks.sup.2)+(ks.sup.2 *kp.sup.2)+2*kp.sup.2 
*ks.sup.2 *cos (P)] (18) 
and 
EQU I.sub.2 =C * [(ks.sup.2 *kp.sup.2)+(kp.sup.2 *ks.sup.2)+2*ks.sup.2 
*kp.sup.2 *sin (P)] (19) 
By viewing equations 18 and 19 it is evident that with this invention, the 
amplitude A portion is always proportional to the average intensity DC 
level, a feature assumed by prior art in equations 2 and 3, but not 
usually true because of scale imperfections; thus: 
EQU A=DC=2*C*kp.sup.2 *ks.sup.2 (20) 
further, the signal I.sub.3 becomes 
EQU I.sub.3 =D(kp.sup.2 ks.sup.2 +ks.sup.2 kp.sup.2)=2*D*kp.sup.2 *ks.sup.2(21) 
Thus, the signal I.sub.3 will be directly proportional not only to the 
average intensity DC level, but also to the amplitude A, independently of 
the polarization effect of the diffraction grating 16 The amplitude need 
not always equal the DC level as indicated by equation 20, rather, it is 
sufficient if the amplitude is proportional to the DC level. Thus, if one 
of the polarizers or half-wave delay plates are not perfectly matched in 
their transmission qualities, the DC level will be proportional to the 
amplitude rather than equal to the amplitude but may still be used to 
provide feedback. The DC level can therefore be used for measuring the 
amplitude A in an automatic gain control system for keeping it a constant 
value using a feedback loop and amplifier. 
As illustrated in FIG. 3b, the amplitude A is equal to the average DC 
level, as shown in equation 20. The average intensity, that is, the DC 
level, can now be used for measuring the amplitude A in an automatic gain 
control system to keep the amplitude a constant value. A feedback loop and 
amplifier, both well-known circuit elements in the prior art, may be used 
to ensure that the amplitude A remains a constant value, independent of 
the polarization effect of the diffraction grating. 
As previously stated, when such a feedback was used in the prior art, it 
unfortunately had the effect of compounding the error because the 
amplitude A was not directly proportional to the DC level if the 
diffraction efficiencies were different. 
A further advantage of rotating the polarization direction of the beams in 
between each point where the beams 17 and 18 strike the grating scale 16, 
as shown with respect to FIG. 4a, is the elimination of errors due to a 
phase shift that a beam undergoes at each diffraction. At a diffraction, 
the output beam will be phase delayed relative to the input beam. The 
phase delays are different for the p- and s-polarized beams. If detection 
is made according to the prior art, this phase difference .DELTA.P will 
add to the phase difference P between the element beams as the grating is 
displaced. If .DELTA.P varies over the scale area, which is usually the 
case because of imperfections in the scale, there will be an error in the 
measured displacement based on phase changes not caused by scale 
displacement. By forcing the diffracted beams to be p-polarized at one 
diffraction and s-polarized at the other diffraction, the phase difference 
.DELTA.P is effectively eliminated according to the invention. Therefore, 
there are no scale displacement errors originating from phase shift caused 
by the diffractions, a further advantage of the invention over the prior 
art. 
According to principles of the invention, a single beam impinges on the 
scale, at a single point. The scale itself splits the beam and, upon 
impinging a second time, combines the beam into the beam for sensing. Use 
of a single beam, striking a single point, assures uniform scale 
conditions for each of the two diffracted beams. When the reflected beams 
strike the scale, they both strike at the same point, once again assuring 
uniform scale conditions at the critical point. The scale itself is the 
beam splitting and combining element, by selecting two of the diffractions 
from the scale. Using a single incident beam and the scale itself as the 
splitting and combining element is a simple design with much less chance 
of introducing errors. 
FIGS. 4b-4d illustrate alternative positions for the polarizer 28 and the 
delay plate 62. As illustrated in FIG. 4a, the preferred position for the 
polarizer 28 and half-wave delay plate 62 is after the reflector 27, to 
reduce the effect on the light beam 37 caused by reflector 27. However, in 
some embodiments, it may be desired to modify the polarization of the 
light prior to it striking the reflector 27. As illustrated in FIG. 4b, 
the polarizer 28 and half-wave delay plate 62 are positioned in beam 18, 
prior to it striking the reflector 27. The polarization of the light beam 
is modified in the manner that has been explained with respect to FIG. 4a. 
The light beam 37 then returns to the diffraction grating 16 and is 
diffracted a second time, according to the principles previously 
described. 
FIG. 4c illustrates the embodiment in which the polarizer 28 is positioned 
prior to the reflector 27 and the half-wave delay plate is positioned 
after the reflector 27. The output beam 37 will be modified as previously 
described with respect to FIG. 4a assuming that the reflector 27 does not 
modify the polarization of the beam. FIG. 4d illustrates the polarizer 28 
extending across both beams 18 and 37, both before and after reflection 
from reflector 27. The light then enters half-wave delay plate 62 to 
provide the output beam 37, as previously described. The alternative 
embodiments of FIGS. 4b-4d may be desired in some circumstances to ensure 
proper modification of the polarization of the light beam 18 prior to 
being diffracted a second time. 
The order of the polarizers and half-wave plate may be switched if desired. 
For example, the half-wave delay plate 62 may be positioned in the beam 
prior to the polarizer 28. The variations shown in FIGS. 4a-4d are also 
applicable to the delay plate 62. The delay plate may be positioned in the 
beam prior to the polarizer, either before or after the reflector. A 
quarter-wave delay plate may be used which spreads both beams 18 and 37 
prior to and after reflection, similar to that shown for polarizer 28 of 
FIG. 4d. The wave will be effectively rotated as by a half-wave delay 
plate because it passes through a quarter-wave delay plate twice. Other 
modifications could also be made which fall within the scope of this 
invention. 
One drawback of the system and method described with respect to the prior 
art at FIG. 1 and the inventive system of FIG. 4a is that significant 
light is lost as the polarizers 26 and 28 screen light not having the 
desired polarization. 
FIGS. 5 and 6a-6e illustrate a system and method for providing two 
reflections from the grating 16 in which the polarization effect of the 
scale grating is canceled and the beams are polarized perpendicular to 
each other after striking the scale a second time so that they do not 
interfere in the output beam 68. A .lambda./2 delay plate 70 is placed in 
the path of the left-hand diffracted beam 76. Two .lambda./2 delay plates 
72 and 74 are placed in series in the path of the right-hand beam prior to 
its striking the grating 16 a second time. The fast and slow axis of the 
respective .lambda./2 delay plates 70, 72, and 74 are selected to mirror 
the polarization about a selected axis. 
FIGS. 6a-6e illustrate the beam at different stages in the system of FIG. 
5. (The polarization of a light beam is treated as a vector and vector 
mathematics apply to changes in the polarization.) As previously stated, a 
.lambda./2 delay plate has the effect of producing a mirror image of the 
polarization of a beam about its fast axis. The polarization of the input 
beam 15 is denoted by E.sub.i of FIG. 6a having an angle 
.beta.=45.degree.. 
As is known in vector mathematics, the polarization vector E.sub.i of the 
input beam 15 can be divided into the two components E.sub.ip, which is 
the component parallel to the grating grooves 20, and E.sub.is which is 
the component perpendicular to the grating grooves 20. When the input beam 
15 strikes the diffraction grating 16 at point 13, two diffraction beams 
are created, a left-hand beam 76 and a right-hand beam 78. As previously 
stated, the negative angle diffraction beam is referred to as the 
left-hand beam and the positive angle diffraction beam is referred to as 
the right-hand beam for ease in understanding and reference. The left-hand 
beam 76, as shown in FIGS. 5 and 6b, has a polarization vector E.sub.l, 
(for E.sub.left-hand), and an angle with respect to the parallel 
direction. .alpha. is an arbitrary angle based on the difference in the p- 
and s-diffraction efficiencies. If the p- and s-diffraction efficiencies 
are equal, the angle .alpha. will be 45.degree.. However, the p- and 
s-diffraction efficiencies are generally not equal, and thus the angle 
.alpha. is an unknown value and may be greater than or less than 
45.degree.. Similarly, the right-hand side of the diffracted beam 78 will 
have a polarization direction denoted as E.sub.r of the beam 78 at the 
same angle because both beams impinged upon the grating 16 at the same 
place and having the same polarization upon striking the grating 16. 
The right-hand beam 78 is then reflected by retro-reflector 25 and directed 
toward the first .lambda./2 delay plate 72. As illustrated in FIG. 6c, the 
.lambda./2 delay plate 72 is oriented with its fast axis perpendicular to 
the diffraction grating grooves 20. The polarization of the beam 78 is 
therefore mirrored about the perpendicular axis component to rotate the 
polarization E.sub.r into a mirror image about the perpendicular 
polarization. The beam 80 exiting from the .lambda./2 delay plate 72 has 
the polarization as illustrated in FIG. 6c. The beam 80 then enters the 
second .lambda./2 delay plate 74. As illustrated in FIG. 6d, fast axis of 
the .lambda./2 delay plate 74 is oriented 45.degree. from the parallel to 
the grating grooves 20 and thus mirrors the polarization of beam so into 
the polarization of the output wave 82. 
A mirror image of the polarization of the left-hand beam is created by 
orienting the fast axis of the .lambda./2 delay plate 70 at 45.degree. 
from the parallel to the grating grooves 20 to create a mirror image 84 of 
the beam 76. As shown in FIG. 6d, output wave 84 now has a polarization at 
an angle .alpha. with respect to the perpendicular vector. 
The polarization components both parallel and perpendicular to the grating 
grooves have their amplitudes reversed by the two .lambda./2 plates as can 
be seen by comparing FIG. 6b to FIG. 6d. Thus, when the beams 82 and 84 
strike the diffraction grating 16 a second time, the effect of the 
differences in the s- and p-polarization efficiencies will be canceled. 
The respective beams 82 and 84 strike the diffraction grating at a second 
point 24 and are diffracted into new output beam 68. The output beam 68 is 
the combination of the left and right-hand beam shown in FIG. 6e. The 
differences in the s- and p-polarization diffraction efficiencies have 
been canceled, and thus the right-hand component and the left-hand 
component have an equal magnitude and are polarized 90.degree. from each 
other. Further, the polarization of the left-hand beam and the right-hand 
beam are different by 90.degree. and thus they will not interfere when 
combined into a single beam, a desired characteristic. 
All changes in the phases of the output signals are the result of 
displacement of the diffraction grating 16 as the object 23 moves, rather 
than errors in the scale, and thus an accurate measure of displacement can 
be made. Equations 16-21, described with respect to the device of FIG. 4a, 
may then be used to determine the actual displacement. However, the actual 
intensity of the signals will be significantly greater because polarizers 
are not used. The intensity of the respective beams I.sub.1, I.sub.2, and 
I.sub.3 is more than double the corresponding intensity of the beams when 
polarizers are used. 
A further drawback of prior art devices is that they cannot be used on 
scales with a pitch smaller than the wavelength of the light source. 
Presently, laser diodes having a wavelength of approximately 780 nm are 
used as the light source. The minimum scale pitch which may be used is 
approximately 1 micron. 
According to an alternative embodiment of the invention, a position sensor 
has an input beam 92 at an angle .theta. with respect to the 
perpendicular, as illustrated in FIGS. 7a and 7b. (FIG. 7a is the top view 
of FIG. 7b, and thus illustrates that the light source is horizontally 
offset from the respective retro-reflectors.) A monochromatic light source 
90 projects a collimated beam 92 onto the diffraction grating 16 at an 
angle .theta. with respect to the perpendicular 94 to the surface of the 
grating 16. The beam 92 is diffracted into a zeroth order diffraction beam 
96 and a first order diffraction beam 98 (right and left beams, 
respectively). The zeroth order beam 96 and the first order diffraction 
beam 98 are reflected back to the diffraction grating 16 by 
retro-reflectors 100 and 102, respectively. The two reflected beams 104 
and 106 are parallel to the respective diffracted beams 96 and 98 so that 
they strike the scale at a point 108 offset from the point 91 at which the 
input beam struck the scale. At point 108 the diffracted beams are 
diffracted a second time and joined into a single output beam 110. The 
output beam 110 is analyzed by the photodetector circuitry 11 of the same 
type as shown in FIG. 2c. The polarizers 114 and 116 and .lambda./2 delay 
plates 118 and 120 have the same function as previously described with 
respect to FIG. 4a. An arrangement in which only .lambda./2 plates are 
used as described with respect to FIG. 5 may also be used. 
The relationship of the impingement point 91 of the input beam to the 
impingement point 108 of the reflected beam may be selected to provide 
desired features in reading the scale. As illustrated in FIG. 7a, the 
input point 91 and output point 108 are spaced from each other 
perpendicular to the direction of the scale grating grooves 20. (The scale 
grating grooves 20 are shown significantly enlarged for illustration 
purposes only to provide a clear view of their direction. In an actual 
device, the pitch of the individual grating is about 1 micron, and the 
diameter of the impingement points 91 and 108 will be sufficiently great 
to cover thousands of grating grooves 20.) The impingement points 91 and 
108 must be spaced apart to ensure that they do not overlap. The area 
covered by the beams may take up significant scale area. FIG. 7c 
illustrates the same read head as FIG. 7a; however, reflectors 102 and 100 
are oriented so that the impingement points 91 and 108 are placed 
laterally from each other and parallel to the grating grooves 20, rather 
than along the movement of the scale direction. The configuration of FIG. 
7c permits a somewhat longer measurement range for a fixed scale length 
because of the more narrow beam footprint in the direction of scale 
movement, but requires a wider scale. 
The advantages of having the incident beam 92 at an acute angle can be best 
understood by examining the principles of physics with respect to light 
striking a diffraction grating. The angle at which the light is diffracted 
from the grating is given by the equation: 
EQU Sin .theta..sub.i +Sin .theta..sub.0 =n * .lambda./p (22) 
where .theta..sub.i is the angle of the incident beam with respect to a 
plane which is perpendicular to the grating 16 and parallel to the grating 
grooves 20, .theta..sub.0 is the angle of the diffraction beam relative to 
the same plane, n is the order of the diffraction, .lambda. is the 
wavelength of light, and p is the grating pitch. For a beam whose 
incidence is normal to the surface, Sin .theta..sub.i =0. Equation 22 for 
a beam normal to the surface becomes, for the first order of diffraction, 
Sin .theta..sub.0 =.lambda./p. For a wavelength of light of 0.78 microns 
and a pitch of 1 micron, the angle .theta..sub.0 =51.26.degree.. For a 
pitch of 1.5 microns, .theta..sub.0 =31.degree., but for a pitch of 0.8 
microns, .theta..sub.0 =77.degree., and for a pitch of 0.78 microns, 
.theta..sub.0 =90.degree., a difficult position to place the reflectors 
and sensors. If the pitch becomes less than 0.78 microns, Sin 
.theta..sub.0 must become greater than one, an impossibility, and the 
first order diffraction essentially disappears. For this reason, the pitch 
must remain somewhat greater than the wavelength of incident light to 
ensure an adequate diffraction angle if the incident beam is normal to the 
surface. 
An advantage in using a small pitch is that scale linearity is 
significantly improved. When manufacturing a scale, one is often less 
concerned about the full scale accuracy than one is about the scale 
pattern linearity. The reason for being concerned about the scale pattern 
linearity is that an erroneous scale factor can be corrected fairly easily 
in the electronics by a multiplication of each reading by a single 
calibration factor; however, a linearity error requires an individual 
calibration value for each scale point, the calibration factor being 
difficult to determine. The holographic method of manufacturing scales is 
capable of yielding scales with a high degree of linearity. The linearity 
depends mainly on the surface quality of the mirrors Imperfections in the 
mirror surfaces distort the wave fronts from being perfectly flat. A 
deviation d in a wave front results in an error e as follows: 
EQU e=(d/.lambda.g)*p 
where .lambda.g is the wavelength of the light source which is used to 
generate the scale, and p is the scale pitch. From this equation, it can 
be seen that the linearity error is directly proportional to the scale 
pitch. The smaller the scale pitch, the smaller the linearity error for 
holographically manufactured scales. 
The advantage of the read head of FIGS. 7a-7c can be seen again by 
examining the basic diffraction equations. 
EQU Sin .theta..sub.i +Sin .theta..sub.0 =n * .lambda./p 
where n is the order of diffraction of the diffracted light, .theta..sub.i 
is the angle of incident light, and .theta..sub.0 is the angle of 
diffracted light. If .theta..sub.i is set equal to .theta..sub.0 (rather 
than equal to zero), then the equation becomes: 
EQU Sin .theta..sub.0 +Sin .theta..sub.0 =n * .lambda./p; 
or 2 Sin .theta..sub.0 =n * .lambda./p; 
which yields 
EQU Sin .theta..sub.0 =n * .lambda./2p. 
The pitch can therefore be made twice as small as was possible in the prior 
art, and still achieve the same diffraction angle .theta..sub.0 for a 
given wavelength of light. Setting the angle .theta..sub.i of the input 
beam 92 to be equal to the angle .theta..sub.0 of the first order 
diffracted beam 98 also ensures that there will be no error in the 
measured scale displacement due to a scale run out in a direction 
perpendicular to the scale surface 16. 
A further advantage of the read head of FIGS. 7a-7c is that the incident 
beam is not normal to the surface, thereby avoiding the problem with light 
that is reflected back into the light source 10 of FIG. 1 of the prior 
art. Back-reflected light generates noise in the laser diode beam, and 
consequently in the scale output beam. Another advantage is the 
elimination of the effect of harmful multiple reflections within the read 
head which otherwise can be a problem in a perfectly symmetrical 
configuration as in the read head according to the prior art of FIG. 1. 
Even if the polarizers at the retro-reflectors block the zeroth order 
beams originating from the second diffraction, that is when the beams 
coming from the retro-reflectors strike the scale again, the second order 
diffracted beams generated at that point will retrace the respective beam 
paths back into the laser diode light source 10, thereby disturbing it. 
Having the light source 10 at an angle avoids these problems. 
With an inclined incident beam, as described above, the resolution of the 
output signal from the detector is p/2, where p is the scale pitch. For a 
scale with 0.5 micron pitch the output resolution would be 0.25 micron per 
output signal period, i.e., the same as for a scale with 1 micron pitch 
and an input beam of normal incidence. The advantage with the smaller 
scale pitch is that a better scale linearity can be achieved. If desired, 
the beam 98 can be selected as the second order diffraction beam instead 
of the first order diffraction beam. For a given scale pitch one is again 
able to obtain a resolution of p/4 per output signal period, i.e., the 
same as for reading the scale with a beam of normal incidence. 
The read head principle described with respect to FIGS. 4a-7c is also 
suitable for a read head used in an x-y displacement measuring device. The 
principles outlined with respect to FIGS. 7a-7c are illustrated in an x-y 
encoder in FIGS. 8a and 8b. FIG. 8a is a top plan view of an x-y decoder 
read head. The read head is basically two separate linear read heads 
impinging on gratings perpendicular to each other, each grating being 
perpendicular to the measured direction of displacement. That is, light 
from light source 121 measures displacements in the x-direction in 
conjunction with detector 11 and light from source 124 measures 
displacements in the y-direction in conjunction with photodetector system 
12. 
The same principles previously described with respect to FIGS. 7a-7c are 
applicable to the embodiments of FIGS. 8a and 8b. Light from source 121 
impinges at point 128 and is diffracted into the respective diffraction 
beams and reflected back to point 130 by reflectors 117 and 119. It is 
diffracted a second time and sensed by detector 11, in a manner similar to 
that which has previously been described. Similarly, light from light 
source 124 is diffracted at point 132 to retro-reflectors 136 and 138 for 
reflection to point 140 where the beam is diffracted a second time and 
sensed by detector 12. The beams pass through appropriate polarizers and 
.lambda./2 delay plates as previously described with respect to FIGS. 
7a-7c, the same components bearing the same reference numbers. 
In the embodiment of FIG. 8a, the relationship between the impingement 
points 128 and 130 is along the respective direction of the scale 
movement, the x-beam being spaced laterally in the x-direction along the 
scale. Similarly, the two impingement points of the y-beam 132 and 140 are 
spaced laterally along the y-direction of the scale. In the embodiment of 
FIG. 8b, the light sources 121 and 124 and the retro-reflectors 117, 119, 
136, and 138 are oriented to cause the respective impingement points on 
the scale to be perpendicular to the respective scale direction, similar 
to that described with respect to FIG. 7c. 
FIG. 9 illustrates a design in which a single light source is used for an 
x-y displacement sensing device. The previously two separate light sources 
are merged to a single light source 141 and one retro-reflector 142. The 
function of the single light source x-y position detector is the same for 
measurements in both directions and similar to that previously described 
with respect to FIGS. 4a-8b. The working principle will first be described 
with respect to displacements in the x direction. 
The monochromatic and collimated input beam 146 from laser diode 141 is 
linearly polarized with its polarization direction at a 45.degree. angle 
to the p- and s-polarization directions for the gratings on the scale 16. 
The beam lies within a plane which is perpendicular to the scale and makes 
a 45.degree. angle to both the x-z and y-z planes. As shown in the 
coordinate system of FIG. 9, the z-axis is perpendicular to the plane of 
the paper. The input beam is then symmetrically shared between the x and y 
measurement directions. The beam 146 is diffracted at point 148 into a 
zeroth order beam 150 and two first order beams 151 and 152. The zeroth 
order beam 150 is reflected by retro-reflector 142 to point 154. (In the 
top plan view of FIG. 9, the beam 150 and the reflected beam 153 appear to 
coincide, but in fact they are vertically offset from each other by 
retro-reflector 142 and are separated, as would be apparent in side view.) 
Reflected beam 153 passes through polarizer 156 and .lambda./2 delay plate 
158 to rotate the polarization direction 90.degree.. At point 154, the 
beam is diffracted a second time for combining into a beam with the x- and 
y-diffraction beams for detecting displacement. 
Displacement in the x direction is measured using a combined beam 164 from 
the first order beam 152 as reflected and modified into beam 155 and beam 
153. The beam 152 is reflected by retro-reflector 162 to pass through 
polarizer 143 and .lambda./2 delay plate 145 to return as beam 155 and 
impinge upon point 154 for a second diffraction. The zeroth order 
diffracted beam, reflected back as 153, is combined with the first order 
diffraction reflected beam 155 into a combined output beam 164, each of 
the element beams having orthogonal polarization directions so they do not 
interfere with each other as described with respect to FIG. 4a. The beam 
164 is reflected by the half-mirror 169 and is picked up by the x-detector 
168 The x-detector 168 is similar to the configuration shown and described 
with respect to detector 11 of FIG. 1. Linear displacements in the 
x-direction are thus sensed. 
The y-displacements are sensed in a similar manner to the x displacement. 
The input beam 146 is split into respective diffractive beams 150 and the 
other first order diffraction 151. The beam 151 is reflected as beam 157, 
passing through polarizer 161 and halfwave delay plate 163. Beam 157 is 
diffracted a second time and combined with beam 153 to form an output beam 
170 for detection by y-detector 172 to sense displacement in the 
y-direction. The angle .theta..sub.i (see FIG. 10) between the input beam 
and the scale is selected as follows: 
##EQU1## 
where .lambda. is the wavelength of the light source and p is the scale 
pitch. With this choice of .theta..sub.i, the angles between the first 
order diffracted beams and the scale will be equal to .theta..sub.i. This 
aids to eliminate error in the measurement caused by scale runout in a 
direction perpendicular to the scale's surface. The impingement points 148 
and 154 are selected to be diagonally spaced from each other along the 
square grid pattern of the x and y diffraction gratings If no polarizers 
are used, as in the embodiment of FIG. 5, the beam intensity as sensed 
will be equal to that sensed with two light sources. 
FIG. 10 illustrates an apparatus having the principles of the invention 
similar to those of FIG. 7, in which the diffraction grating 16 is a 
transmission grating rather than a reflective grating. The use of a 
transmission grating per se is well known in the art and, given the 
teachings herein, it would be possible to build the system using a 
transmission grating rather than a reflection grating for the diffraction 
member 16. In summary, the light beam 92 impinges upon the diffraction 
member 16 at an initial angle .theta..sub.i. The light is diffracted in a 
zeroth order beam 96 and a first order beam 98. These beams are 
transmitted through the scale 16 rather than being reflected. The 
reflectors, polarizers and half-wave plates are on the opposite side of 
the diffraction grating 16 from the light source 10 and operate as 
previously described with respect to FIGS. 4 and 7, common reference 
numerals being used for similar elements. After the light beams are 
diffracted a second time, the combined beam is provided to detector 11, as 
previously described. 
FIG. 11 illustrates a diffraction member 16 being a transmission member and 
having a pattern painted or etched on the surface thereof. The operation 
of the structure of FIG. 11 is similar to that of FIG. 4 except for the 
use of transmission member 16 and, given the description previously 
provided herein, will be apparent to those of ordinary skill in the art. 
Different diffraction members and grating elements may be used, including 
any available transmissive or reflective diffraction members. Any suitable 
diffraction member or grating element may be used of those presently 
available in the art. The grating may be a surface relief grating, a photo 
emulsion grating, a thin grating, or a phase grating. For example, surface 
relief grooves and painted patterns have been shown, but any element which 
provides a suitable diffraction of light may be used. 
The invention has been shown and described with respect to various 
embodiments. It will be clear that the particular features discussed with 
respect to FIG. 5 may also be used in the embodiments illustrated in the 
other figures, according to the principles of the invention. While the 
principles of the invention have been primarily illustrated by describing 
linear encoders and sensing linear motion, rotational encoders or sensing 
of rotational motion may also use the principles of the invention and fall 
within the scope thereof as encompassed in the claims. Similarly, many 
variations in the structure or method may fall within the scope of the 
claims, the scope being limited only by the claims and not the detailed 
description of particular embodiments.