Patent GB-1014785-A (GB)
Title: Improvements relating to fourier transform optical object analysers
IPC: G06E3/00
Filed: 1963-07-18
Abstract: 1,014,785. Electric analogue calculating; recording and playback. OFFICE NATIONALE D'ETUDES ET DE RECHERCHES AEROSPATIALES. July 18, 1963 [July 18, 1962], No. 28487/63. Headings G4G and G5R. A Fourier transform analyser for optical analysis of a plane luminous or transparent object and for translating the result of the analysis into time dependent electrical signals comprises a support for the object to be analysed, a mask having a rectilinear slit enabling light rays from a line of the object to be projected therethrough, means for step-by-step shifting of the mask to sequentially unmask the object lines through the slit, a variable transparency pattern grid including alternate transparent and opaque regions which are bounded by curves spaced equally along straight lines parallel to the slit with the specific curve spacing along such lines varying according to a law such that the reciprocal of the spacing along a straight line falling within the slit at a given time is proportional to such time, means for continuously shifting the pattern grid with respect to the object support and in front of the same along a perpendicular to the slit, according to a movement having a given kinematic equation related to time, and photo-electric means collecting the light rays emergent from the object through the pattern grid and slit for each continuous shift of such pattern grid. An object 12 inscribed on a support 13 (Fig. 1a), e.g. of frosted glass and illuminated by light transmission or reflection is superimposed with a mask 11 (Fig. 1b), having a slit to define a line of the object 12; and a pattern grid (Fig. 1c) is moved with uniform velocity perpendicularly to the linear slit and parallel to a column of the object 12. The pattern grid is a transparent plate with a family of equilateral hyperbolµ 2 1  to 2 n  and 2 -1  to 2 -p  inscribed thereon with respect to coordinate asymptotic axes Ox, Oy parallel to the linear and columnar axes of object 12; the equations of the hyperbolµ being with respect to integral parameter D. A straight line 3 of abscissa x cuts the hyperbolµ at intersection points A 1  to A n  whose ordinates are given by and cuts the x axis 2 0  at A 0 . The segments A 1 , A 0  . . . A n , A n-1  are equal and the common 2D<SP>2</SP> segmental length -is inversely proportional to x displacement x of line 3 from axis Oy. Similarly, a straight line 4 of ordinate y is divided into equal segments B B 0 , B 2  B 1  . . . B n  B n-1  where line 4 intersects axis Oy at B 0 . Thus the pattern grid is defined by spatial frequency #(x) = <SP>x</SP>/ 4D2  along line 3 of abscissa x and by a spatial period of 4D2/x0 along abscissa x 0 . The regions between contiguous hyperbolµ are alternately blackened and left transparent and are anti. symmetrical with respect to the co-ordinate axes. The pattern grid may alternatively (Fig. 1d, not shown), be symmetrical with regard to the co-ordinate axes. The transparency is illuminated by lamp 14 (Fig. 2). The slit 10 of the mask is aligned with asymptotic axis Ox of the grid and the latter is moved parallelly to the Oy axis at uniform velocity v, such that y = vt, while the emergent light is focused on a linear photo-cell 16 whose output is amplified and applied to recording means 18. Then if γ is the transparency function of the grid given by and 2γ is a time function of frequency and the photo-cell output is given by where v 1 , v 2  are time frequencies corresponding to abscissµ which define the width of the slit 10, so that the output represents the Fourier transform of the odd portion of the real luminance or transparency function of a line of the object; the corresponding transform of the even portion being obtainable by substituting the pattern of the grid of Fig. 1d for that of Fig. 1c. The resolving power of the system is computed by mathematics. In a modification, a two-dimensional Fourier analysis may be effected without using the slit; the pattern grid being traversed from a starting point in which the asymptotic axis Ox coincides with the left vertical edge of the object to be analysed, and between each scan of the pattern grid, the latter is displaced one step along the x axis perpendicularly to the scanning movement, which is thus two-dimensional. The two dimensional luminance or transparency functions of the object 12 is given by the sum of N one dimensional function of y, i.e. each function representing light intensity distribution along one of the N columns of the object. If plate 13 (Fig. 1a) is rectangular or square and of side L perpendicular to the scanning movement, the steps of the pattern grid are given by between two successive continuous shifts are L/N since there are N columns of the object and N scans, so that D<SP>2</SP> = L2/4N if each step equals the pitch of the grid pattern along line x = L, and the above equation becomes Fig. 5 shows a pattern grid of area 4L<SP>2</SP> comprising two identical symmetrical rectangular pattern grids of area 2L<SP>2</SP> having a common side parallel to Oy, which is reciprocated N times with uniform velocity across the front of the object in direction Oy with amplitude L from a position in which the x axis of the grid and the left vertical side of the object are coincident; L the grid being shifted one step - along the x N axis between reciprocations; the object coinciding with the right upper quarter of the grid (13<SP>1</SP>) during the 1st scan and coincident with position 13<SP>N</SP> during the Nth scan; the columnar divisions of the object being 8 in number, indicated in the margin of Fig. 5 with corresponding space frequencies. For the first scan, column 1 is scanned at space frequency 1 zero, column 2 at space frequency -and column L 7 8 at space frequency - and for the 8th scan, L 1 column 1 is scanned at space frequency -, L 2 column 2 at space frequency -and column 8 at L space frequency O. E.g. column 5 is scanned successively at space frequencies 4/L,   3/L, 2/L, 1/L,   O, 7/L, 6/L, 5/L. If m is the number of the scan, and i the number of the column, the output signal for the mth scan is function Fm(y) over the interval O, L given by the sum of N components representing the respective contributions of the N columns. and it is shown that where and a signal representing f mi (y) is obtained and stored at each scan to synthesize the function and the luminance or transparency function B(xy) = b 1 y+b 2 y+ . . . +b i y+ . . . b 1 y (6) and it is shown by mathematics that the total output signal Fm(y) is the sum of N sine signals of N frequencies a m,1 ; a m,2 ; . . . a m,i  . . . a m,N  separable by a Fourier analysis of Fm(y) to N pairs of amplitude terms A m,i  and B m,i  constituting information on the successive columns of the object. The series of values A 1i,  B 1i ; A 2i , B 2i ; A 3i , B 3i  . . . A mi , B mi  . . .A Ni , B Ni  are shown to form N real and imaginary values of the amplitude of the Fourier transform of b 1 (y) which may be written In operation, the output signals obtained over the first to eighth columnar scans are recorded on tape, and the tape is separated into sections 71 1  to 71 8  (Fig. 18), corresponding to the several scans which are driven in synchronism to traverse reading heads 72 1  to 72 8 , whose outputs are connected to inputs of a rotary switch 74 indexed one step after each scan. The outputs 75 1  to 75 8  of the switch are respectively connected to a low pass filter 76 0  and seven bandpass filters 76 1  to 76 7  tuned to time fre-   quency frequencies O 1  v/L ... 7v/L with their outputs parallel connected to terminal 77 1  at which successively appear during the first to eighth scans the Fourier transformers of the output signal corresponding to the first to eighth columns of the object. Alternatively, the undivided type is looped and equally distributed around eight recording heads. Figs. 3a to 3c show a device for displacing the image carrier and the pattern grid relatively to the mask. Grid 1 is secured to bracket 19 having a pin following screw 21 having threads in opposite directions, which is rotated by motor 22 in two bearings carried by mask 11; the bracket being arrested at each end of its travel by stops 23, 24 effective to rotate the pin about its longitudinal axis to engage the alternate thread of screw 21, whereby the direction of grid traversal is reversed; the threads having different pitches so that the forward movement is faster than the backward movement for each traverse. Mask 11 has an inner aperture 25 carrying a shutter plate 26 movable to mask and unmask slit 10 under control of levers 27, 28 connected by rod 29 and rotatably operated by the grid by means of pin 30 at each end of its traversal; lever 27 being linked over cable 31 to the shutter plate so that the latter is open during the forward motion of the grid and closed during its backward motion. An escapement 36 (Fig. 3c) drives pinion 37 rotatably mounted on mask 11 to engage rack 38 attached to the object support 73, biased by spring 39, and is actuated by lever 35 each time the grid 1 returns to a new scan, and the escapement advances support 13 by one step perpendicularly to the scanning direction. Fig. 4 shows a modified one dimensional analyser having an object support 13 which may be, e.g. a frosted glass on which images are focused, a photographic slide, or a frame for photographic positives the image of which is projected on to photo-cell 16 through kinematograph film 40 looped over spools 41, 44 and driven continuously by motor 45 and sprocket 49. A plate 48 with horizontal slit 49 is steppedly moved by maltese cross, rack-and-pinion action 46, 50, 51, while a rotatory shutter driven by the motor closes the slit while plate 48 is advanced one step. The film (Fig. 6) comprises plural frames g 1 , g 2 , g 3 , g 4  &c. patterned with the grid of Fig. 1c having the x axis horizontal and perpendicular to the motion; the