Patent GB-1317553-A (GB)
Title: Apparatus for generating an image of an object
IPC: G01S13/90
Filed: 1969-04-30
Abstract: 1317553 Simulating image reconstruction EMI Ltd 9 July 1970 [30 April 1969] 21944/69 Heading G4G [Also in Division H4] When optically reconstructing an image from a holographic transparency using a beam of reference radiation, the light intensity at any point Q in any given image plane is determined by the sum S = #X P cos(# P  - (2#)/(#)L PQ ) where X P  is determined by the amplitude of the reference beam and by the density of the transparency at a point P, # P  is the relative phase of the reference beam at the point P and is determined by the angle of the beam and the position of P, # is the wavelength of the reference beam and L PQ  is the distance from P to Q. Given the co-ordinates and X P  for every point P, it is also possible to compute S for every point Q using the fact that S is the real part of #α P .B PQ , where α P  = X P C<SP>i</SP>#<SP>P</SP> and B PQ =e - (2#i)/(#)L PQ , but for a hologram and image each consisting of a rectangular matrix of k x I points for example, the large number of k<SP>2</SP>l<SP>2</SP> values of the transfer factor B PQ  must be stored in the computer. The Specification relates to the fact that by generating points Q sequentially i.e. using a k Î l array of transfer factors B PQ  at a time, it is possible to reduce the total number of stored factors B PQ  since some values can be made common to more than one array. Thus the distance L PQ  from P(a, b) (i.e. a point P with co-ordinates a, b) to Q(c, d) is the same as from P(a+1, b) to Q(c+1, d) and from P(a, b+1) to Q(c, d+1) for parallel rectangular matrices and the transfer factor arrays for adjacent image points on the same row or column overlap except for the first and last array row or column respectively, so that a (2k - 1) x (2l - 1) array of factors is sufficient to provide an appropriate array for each point Q. Fig. 3 illustrates one apparatus for effectively scanning the α P  matrix over the B PQ  array to give successive line scans of image points Q(2k+ 1) delay lines 14 are provided in series, each of (2l+ 1) equal delay cells, each cell being connected by a further delay line 18, representing the phase angle change (- (2#)/(#).L PQ ), to a single summing amplifier 16. k spaced sets of l trains of signals of the form X P cos# P  are fed in to the first line 14 so that at one instant each set occupies the first I cells of a corresponding line 14 and the sum 5 for Q(1, 1) is then given by amplifier 16. After the time characteristic of one delay cell, Q(2, 1) is obtained, and after a time corresponding to one line 14 Q(1, 2) is obtained. When each signal set lies in two lines 14, the output of amplifier 16 is not used. A similar result is obtained using k sets each of k lines 14 and simultaneously feeding each and every signal into the corresponding one of each set of lines, but this requires k<SP>2</SP>(2l-1) lines 18 instead of (2k - 1)(2l- 1) lines. The lines 18 need only introduce a phase shift where n is integral and 0>#> - 2#, Fig. 3a (not shown), and in a modification, Fig. 3b (not shown), they are omitted. The output of each cell is fed to an amplifier to produce both the cell output and the negated cell output which are fed to opposite ends of a series RC circuit. Suitable values of R and C provide a signal at the R-C junction with the desired phase shift # included. Alternatively the positive and negated cell outputs may be obtained from two identical series of delay lines 14 fed with positive and negative versions of the signal trains X P cos# P , and fed to the RC circuit. In a variant of the method, each point Q may be considered to subtend concentric zones of points P having the same value of #. For example, purely resistive transfers may be effected from only those cells in the delay line system for which # lies within a relatively narrow range, although part of the information is lost thereby. Less information is lost if positive resistive transfer occurs for cells for which 0<( - #)<# and negative resistive transfer when #<(-#)<2# (e.g. by arranging that the delay line system feeds antiphase signals to the transfer resistances at these points). In another variant, the series of signal trains X P cos# P  is sampled in quadrature as to amplitude, and the first and second series of samples are used to amplitude modulate respective oscillatory signals fed to respective systems of delay lines 14. Each system resistively transfers signals to both of a pair of summing amplifiers 16. If the samples are X=X P cos# P  and Y=X P cos(# P + (#)/(2)) the transfer resistances are proportional to cos # and sin # to provide the transformers #(Xcos# - Ysin#) and #(Ycos# + Ysin#) at the outputs of respective amplifiers 16, the output being squared and added to give the image point brightness signal. To allow for positive and negative values of cos# and sin#, each delay line gives positive and negative outputs, or is duplicated for the same purpose. Since the relative phases of all the signals in each delay line system are all the same, the delay lines may be replaced by shift register systems fed with digital signals corresponding to the amplitude of the quadrature samples the transfer resistors being weighted according to the digit place to convert back to an analogue signal at the summing point. A final method described for reducing the number of stored quantities L PQ  or # PQ  depends on the distances from P(α, #) to Q(#, #) and P(α, #+Á) to Q(#, #+Á) being identical if P and Q lie on coaxial annuli, polar co-ordinates being used. In a preferred embodiment, Fig. 4, useful for underwater viewing, an ultrasonic beam from a source 21 is reflected to elements of a sensor array 23. The elements are successively sampled in a manner such that a plane wave normally incident thereon would give identically phased signals at each element. An oscillator 22 driving source 21 also has an output which is phase shifted at 29 under the control of a computer 31 by an amount # P  corresponding to the element being sampled and the resulting signal V 0  (representing the holographic reference wave effectively incident at that element) is fed, together with the signal V from the sampled element, to a detector 28, which provides an output representing the mean value of (V+V 0 )<SP>2</SP> =X P  which is stored in the computer. Each output X P  is digitally multiplied by cos(wt+ # P  - # PQ ) for all points Q, using a reduced number of stored factors # PQ  as described, and the products for each point Q are summed for all P. Each sum is either derived for many values of time t, or two samples in quadrature relation are squared and added to obtain the image brightness at a point Q. The signals from the sensors may be sampled at quadrature intervals, e.g. to give instantaneous amplitudes A and B, and signals Y cos Z generated in response thereto, where Y<SP>2</SP>=A<SP>2</SP>+B<SP>2</SP> and tan Z = A/B.