Method and apparatus for determining and encoding linear position by means ...

What is claimed is:

1. A method of determining the linear position on a first lenticular screen, by using a reference lenticular screen, said screens being arranged parallel to each other with each screen having a plane surface and a convex surface and a principal focal plane and having a plurality of lenticules of similar pitch with longitudinal axes which are parallel to each other, comprising the steps of:

a) directing a collimated beam of radiation perpendicularly into one lenticular screen;

b) allowing the beam transmitted by said one lenticular screen to enter another lenticular screen, with said lenticular screens being spaced in relationship to each other so as to recollimate the radiation beam upon exit from the other sheet;

c) receiving the recollimated beam exiting from the other lenticular screen on a radiation detector which subtends the field-of-view of the lenticules in the other screen; and

d) displacing the lenticular screens relative to each other in a linear direction while sensing the position of the recollimated beam exiting the other screen and calculating the number of lenticules and fractions of lenticules being displaced utilizing the detector array and utilizing means for making such computation.

2. The method of claim 1, wherein said one lenticular screen presents its plane surface towards the incident radiation beam and said other lenticular screen presents it plane surface towards the incident radiation beam and the spacing between the screens is such that the principal focal plane of said one screen substantially coincides with the plane surface of said other screen.

3. The method of claim 1, wherein said one lenticular screen presents its convex surface towards the incident radiation beam and said other lenticular screen presents its convex surface towards the incident radiation beam and the spacing between the screens is such that the principal focal plane of said other screen substantially coincides with the plane surface of said one screen.

4. The method of claim 1, wherein said one lenticular screen presents its plane surface towards the incident radiation beam and said other lenticular screen presents its convex surface towards the incident radiation beam and the spacing between the screens is such that the principal focal plane of said one screen substantially coincides with the principal focal plane of said other screen and is located approximately midway in the spacing between the two screens.

5. The method of claim 1, wherein said one lenticular screen presents its convex surface towards the incident radiation beam and said other lenticular screen presents its plane surface towards the incident radiation beam and the spacing between the screens is such that the principal focal plane of said one screen substantially coincides with the principal focal plane of said other screen and is located approximately in the plane surfaces of both screens.

6. The method of claim 1, wherein the collimated beam of radiation is laser light.

7. The method of claim 1, wherein the radiation detector is a linear array detector.

8. The method of claim 1, wherein the radiation detector is a two-dimensional array detector.

9. The method of claim 1, wherein the beam entering the radiation detector passes through a filter designed to pass substantially all of the wavelengths of the beam and exclude ambient radiation wavelengths.

10. The method of claim 1, wherein the position of the beam exiting the other screen and the number of transits and fractions thereof of the beam across the field-of-view of the lenticules are manually determined.

11. The method of claim 1, in which the determined linear position is encoded using encoding means.

12. The method of claim 11, in which the encoding means is an electronic memory device.

13. The method of claim 11, in which the encoding means is a device making a reference mark on the lenticular screen.

14. The method of claim 1, wherein the position of the beam exiting the other screen and the number of transits and fractions thereof of the beam across the field of view of the lenticules is determined by a microcontroller performing the following steps:

a) determining the beam's position by initially thresholding each element output D.sub.i of the detector array unless D.sub.i is determined to be greater than some threshold value T which may be set at 1/5 of the expected maximum value of D.sub.i with the detector array having n elements indexed from 0 to n-1 subtending the field of view of the lenticular material from left to right; and

b) determining whether there are two possible spots at which the beam could be located, which will occur when the first lenticular screen is near 180.degree. of phase, by computing the quantities ##EQU3## and concluding that if both are zero the spot is near the center of the array, that if both are nonzero the spot is near 180.degree. of phase, and that if only one is nonzero, the spot is near either the left or right ends, where the n detector elements have indexes, i, running from 0 to n-1;

c) using a centroid calculation of ##EQU4## to determine the location of the beam in units of detector elements, where i is the detector element index, and s and f are the start and finish indexes, respectively, and the range is substantially the left half, central half, or right half of the detector for a beam spot in the left, central, or right regions of the detector, respectively, and calculated such that when the beam is near 180.degree. of phase the larger of S.sub.L and S.sub.R can be used to determine which two quadrants to perform the above centroid calculation in, i.e., i=n/2 to i=n for S.sub.L <S.sub.R, and i=0 to i=n/2 for S.sub.L >S.sub.R, but if S.sub.L =S.sub.R the spot is exactly at 180.degree., and if only one of S.sub.L and S.sub.R are non-zero, the centroid calculation is performed in either the left or right halves of the array detector, respectively, and in making these computations the controller continually monitors the value of x and keeps track of how many times the beam has crossed the center of the field-of-view, x.sub.c =n/2, in a given direction, but if the previous value of x is x.sub.p and the number of times that the beam has crossed x.sub.c from left to right from some starting position is N, then N is incremented by 1 if (x.ltoreq.n/2 and x.sub.p <n/2 and (x-x.sub.p)<n/2), N is decremented by 1 if (x<n/2 and x.sub.p .ltoreq.n/2 and (x.sub.p -x)<n/2) and the displacement of the two lenticular screens relative to each other and relative to some starting position in units of the width of a lenticule can be expressed as X=N+(x-n/2)/n.

15. The method of claim 14, wherein the determined linear position is encoded in an electronic memory device.

16. The method of claim 14, wherein the determined linear position is encoded on the lenticular screen by marking means.

17. An apparatus for determining the linear position on a first lenticular screen, comprising:

a) means for producing collimated radiation;

b) a reference lenticular screen with a plurality of lenticules which can be illuminated by the radiation and held in a position oriented substantially perpendicular to the radiation;

c) said lenticular screens having a similar pitch, oriented substantially parallel to each other, and with the axes of the lenticules of said screens being substantially parallel to each other, and spaced so as to recollimate the radiation beam upon exit from the last screen it exits;

d) means for displacing said screens in relation to each other in a linear direction;

e) means for detecting the recollimated beam within the field-of-view of the lenticules;

f) means for determining the position of the recollimated beam within the field-of-view of the lenticules, and keeping account of the number of transits and fractions thereof of the beam across the field-of-view of the lenticules, due to the linear displacement of the lenticular screens relative to each other.

18. The apparatus of claim 17, wherein the means for producing the collimated radiation is a laser.

19. The apparatus of claim 17, wherein the means for detecting the collimated beam is a linear array detector.

20. The apparatus of claim 17, wherein the means for detecting the collimated beam is a two-dimensional array detector.

21. The apparatus of claim 17, which further includes a filter which is designed to pass substantially all of the wavelengths of the beam exiting the last screen and exclude ambient radiation wavelengths before being detected by the detecting means.

22. The apparatus of claim 17, wherein the means for determining the position of the beam exiting the last screen and the means of keeping account of the number of transits and fractions thereof of the beam across the field-of-view of the lenticules is accomplished manually.

23. The apparatus of claim 17, wherein the apparatus has means for outputting the linear displacement of the first screen relative to the reference screen and has means for encoding this linear displacement.

24. The apparatus of claim 23, in which the means for encoding the linear displacement is an electronic memory device.

25. The apparatus of claim 23, in which the means for encoding the linear displacement is a marking device for marking a reference point on the first screen.

26. The apparatus of claim 17, wherein the means for determining the position of the recollimated beam within the field-of-view of the lenticules and keeping a count of the number of transits and fractions thereof of the beam across the field-of-view of the lenticules is a microcontroller programmed to perform the following steps:

a) determining the beam's position by initially thresholding each element output D.sub.i of the detector array unless D.sub.i is determined to be greater than some threshold value T which may be set at 1/5 of the expected maximum value of D.sub.i with the detector array having n elements indexed from 0 to n-1 subtending the field of view of the lenticular material from left to right; and

b) determining whether there are two possible spots at which the beam could be located, which will occur when the first lenticular screen is near 180.degree. of phase, by computing the quantities ##EQU5## and concluding that if both are zero the spot is near the center of the array, that if both are nonzero the spot is near 180.degree. of phase, and that if only one is nonzero, the spot is near either the left or right ends, where the n detector elements have indexes, i, running from 0 to n-1;

c) using a centroid calculation of ##EQU6## to determine the location of the beam in units of detector elements, where i is the detector element index, and s and f are the start and finish indexes, respectively, and the range is substantially the left half, central half, or right half of the detector for a beam spot in the left, central, or right regions of the detector, respectively, and calculated such that when the beam is near 180.degree. of phase the larger of S.sub.L and S.sub.R can be used to determine which two quadrants to perform the above centroid calculation in, i.e., i=n/2 to i=n for S.sub.L <S.sub.R, and i=0 to i=n/2 for S.sub.L >S.sub.R, but if S.sub.L =S.sub.R the spot is exactly at 180.degree., and if only one of S.sub.L and S.sub.R are non-zero, the centroid calculation is performed in either the left or right halves of the array detector, respectively, and in making these computations the controller continually monitors the value of x and keeps track of how many times the beam has crossed the center of the field-of-view, x.sub.c =n/2, in a given direction, but if the previous value of x is x.sub.p and the number of times that the beam has crossed x.sub.c from left to right from some starting position is N, then N is incremented by 1 if (x.ltoreq.n/2 and x.sub.p <n/2 and (x-x.sub.p)<n/2), N is decremented by 1 if (x<n/2 and x.sub.p .ltoreq.n/2 and (x.sub.p -x)<n/2) and the displacement of the two lenticular screens relative to each other and relative to some starting position in units of the width of a lenticule can be expressed as X=N+(x-n/2)/n.

27. The apparatus of claim 26, wherein the apparatus has means for outputting the linear displacement of the first screen relative to the reference screen and has means for encoding the linear displacement.

28. The apparatus of claim 27, in which the means for encoding the linear displacement is an electronic memory device.

29. The apparatus of claim 27, in which the means for encoding the linear displacement is a marking device for marking a reference point on the first screen.