GB Patent 1406889 - VIDEO SIGNAL OUTPUT OF AN OPTO-ELECTRONIC TRANSDUCER TO SIMULATE THE EFFECT OF AN ELECTRICAL FILTER ON SAID VIDEO SIGNAL

Description

PATENT SPECIFICATION

( 21) Application No 37551/72 ( 22) Filed 11 Aug 1972 ( 31) Convention Application No 7111227 ( 32) Filed 14 Aug 1971 in ( 33) Netherlands,(NL) ( 44) Complete Specification published 17 Sept 1975 ( 51) INT CL 2 H 04 N 9/06 9134 9/42/19/52 Index at acceptance H 4 F D 1 A 2 D 1 89 D 1 D 9 D 1 P 9 D 1 Q 2 D 1 Q 7 D 152 D 27 C 1 k D 27 G D 3 GE D 3 OT G 2 J 33 A ( 54) MODIFYING A VIDEO SIGNAL OUTPUT OF AN OPTO-ELECTRONIC TRANSDUCER TO SIMULATE THE EFFECT OF AN ELECTRICAL FILTER ON SAID VIDEO SIGNAL ( 71) We, PHILIPS ELECTRONIC AND ASSOCIATED INDUSTRIES LIMITED, of Abacus House, 33 Gutter Lane, London, E C 2, a British Company, do hereby declare the invention, for which we pray that a patent may be granted to us, and the method by which it is to be performed, to be particularly described in and

by the following statement: -

The invention relates to a method of modifying a video signal output of an opto-electronic transducer to simulate the effect of an electrical filter on said video signal and to apparatus capable of utilizing such a method.

Patent Specification No 1,293,315 discloses a colour television camera employing an opto-electronic transducer in the form of a single camera tube which produces picture signals in a field-sequential manner The picture signals are applied to a field-sequentialto-simultaneous electronic converter provided with a storage device.

The said specification describes two steps which should be taken to enable a cheap store having a restricted frequency range to be used in the electronic converter, whilst enabling a display to be obtained which is rich in detail and which contains different bright (saturated) colours The first step is to optically influence the light emanating from the scene and hence the image of the scene projected onto the camera tube The second step is to electronically process the picture (video) signals produced by the camera tube before they are applied to the electronic converter.

The optical processing is carried out using a rotatable colour filter which is made up of sectors which are each subdivided into portions Each sector comprises a portion which transmits the light from the scene without change in definition and without colour filter effect and a portion which reduces definition and which may include a colour filter The filter is rotated at such a rate that each sector takes one field period to pass the front lPrice 33 Pl of the camera tube The camera tube, which operates by integrating the light from the scene over each field period, thus delivers a composite picture signal in each field period which signal is made up of two components owing to the optical processing These portions are (a) a signal which is restricted in frequency because of the reduction in definition and (b) a signal which is not restricted in this way.

The composite picture signal is then processed by electronic means; it is applied to an aperture correction signal generator which derives a horizontal aperture correction signal from component (b) thereof The aperture correction signal is then added to the composite picture signal in such manner as to restrict the composite picture signal in frequency The composite picture signal so restricted in frequency is then applied to the store in the electronic converter, which produces frequency-restricted but simultaneous picture signals The aperture correction signal, which is and remains field-sequential, is then superposed on these frequency-restricted simultaneous picture signals to achieve horizontal aperture correction.

The use of optical and electronic frequency restriction enables a simple and cheap store to be used in the field-sequential-to-simultaneous electronic converter, whilst still allowing a display to be obtained which is rich in detail and contains different saturated colours.

The reason a frequency restriction is obtained optically is so that a frequency separation can be obtained in the picture signal generated by the camera tube such that the aperture correction signal generator, which gives rise to the electronic frequency restriction, is operative substantially on only the higher-frequency picture signal component of the composite picture signal.

Both optical and electronic frequency restrictions correspond to that given by an electrical filter having a particular transmission ( 52) ( 11) 1406889 m X X c rl 1,406,889 characteristic Owing to the highly different ways in which the two frequency restrictions are obtained, the corresponding filter characteristics may be widely different For example, from the electronic point of view a filter having a continuous characteristic is desirable, and such a characteristic is obtainable optically by means of a ground-glass filter, but these characteristics may still have different forms A given desirable form may be obtained readily by electronic means, but this is not at all the case with an optical filter, in particular a ground-glass filter The ground-glass optical filter diffuses light in all directions, whereas in the camera described only light diffusion in the line scan or horizontal direction is significant as far as the high frequencies are concerned If a diffraction grating is used as the optical filter a reduction in definition in only one direction can be obtained However, the characteristic of the equivalent filter is discontinuous and completely different from the desired continuously varying characteristic.

The invention provides a method of modifying a video signal output of an opto-electronic transducer to simulate the effect of an electrical filter on said video signal, said transducer being of the kind in which an image field is scanned and integration of the effect of the optical input to each point of the image field occurs over a period before the scan of that point, in which method an optical filter is moved through the optical input to each said point of the image field during the integration period corresponding thereto, said filter comprising a plurality of diffraction gratings having differing spacings for reducing the definition in the image field in the immediate scan direction to bring about said simulation.

The invention also provides apparatus comprising an opto-electronic transducer of the kind which operates by scanning an image field and which is capable of integrating the effect of the optical input to each point of the image field over a period before the scan of that point, and an optical filter mounted for motion through the optical input to each said point of the image field during the integration period corresponding thereto, said filter comprising a plurality of diffraction gratings having differing spacings for reducing the definition in the image field in the immediate scan direction to bring about a modification in the video signal output of the transducer, whereby the effect of an electric filter on said video signal is simulated.

It has now been realised that a multiple diffraction grating filter can be used in an opto-electronic converter, because the individual gratings, which have different spacings and hence filter characteristics in each of which the discontinuities are differently located, can together provide a more or less continuous filter characteristic owing to the integration in time which takes place in the converter.

An embodiment of the invention will now be described, by way of example, with reference to the accompanying diagrammatic drawings, in which:

Figure 1 is a block diagram of an optoelectronic converter in the form of a colour television camera, Figure 2 shows signal amplitude/frequency characteristics produced by electric and optical filters, Figure 3 shows part of an optical filter in detail, Figure 4 is a part sectional view which illustrates the relationship between Figures 1 and 3, and Figure 5 shows some curves of signal amplitude versus time and light amplitude versus location.

In Figure 1 an opto-electronic converter in the form of a colour television camera includes an optical filter 1 of a particular form.

Otherwise the camera is for practical purposes the same as that described in detail in Patent Specification 1,293,315 The camera includes a camera tube 2 (which may be of videcon type) having a target 3 An electron beam is produced in the camera tube 2 and is deflected by means not shown so that it scans the target 3 in lines and fields Light L from a scene 4 is projected onto the target 3 via an objective 5 and the optical filter 1 which is rotated by a motor 6 Because of the rotating filter 1 the pick-up tube 2 produces a field-sequential picture signal at a terminal A, a picture signal in a colour determined by the filter 1 being produced during each field period and the entire colour contents of the scene 4 being produced in a cycle of, say, three fields The field-sequential picture signal produced by the camera tube 2 has to be converted if it is to be displayed on a standard receiver utilising simultaneous signals In order to achieve this the terminal A is connected to a terminal D via a circuit 7 which comprises a high-pass filter 8 and a subtraction stage 9 Terminal D is connected in turn to a field-sequential-to-simultaneous electronic converter 10 The circuit 7 introduces a frequency restriction in the picture signal from terminal A which appears at the terminal D, the (electric) filter 8 deriving a high-frequency signal component C from the picture signal at the terminal A this component being then subtracted from the picture signal by the subtraction stage 9.

The converter 10 comprises two stores 11 and 12 and a linear matrix circuit 13 which is switched at field frequency The terminal D is connected directly to one input of the matrix circuit, through the store 11 to a second input thereof and through the series combination of the two stores 11 and 12 to a third input thereof The stores 11 and 12 3 1,0688 each delay the picture signal from the terminal D by one field period Tv and can be simple and cheap, because the picture signal applied to them has a restricted frequency range Because of the presence of the stores the matrix circuit 13 is supplied with three simultaneous signals associated with those colours which are transmitted field-sequentially by the optical filter 1 in a cycle of three fields During the three-field cycle each of the inputs of the matrix circuit 13 is supplied consecutively with three different picture signals each of which occurs during one field period, in order to ensure that a picture signal corresponding to only one colour is always produced at each of the output terminals 14, 15 and 16 of the matrix circuit 13, the circuit 13 includes three switches which switch at the field frequency If picture signals which correspond to the primary colours red (R), green (G) and blue (B), are to be produced at the terminals 14, 15 and 16 respectively, and these colours are transmitted by the optical filter 1 in combination during each field period, rather than separately, the matrix circuit 13 also includes a network of superposition stages which produce the primary colour signals from the combined signals by subtraction and addition.

The output terminals 14, 15 and 16 are connected to inputs of addition stages 17, 18 and 19 respectively, the other inputs of which are connected to the output of the high-pass filter 8 in the circuit 7 (at which the signal C appears) As a result, the addition stages 17, 18 and 19 deliver signals at their output terminals 20, 21 and 22 respectively each of which comprises a frequency-restricted simultaneous signal component provided by the converter 10 and a high-frequency fieldsequential signal component provided by the circuit 7 Displaying the signals which appear at the output terminals 20, 21 and 22 by means of a standard receiver can give a well defined and faithful image of the scene 4, although the converter 10 is only capable of producing signals which when displayed produce an image which is poor in definition.

It will be noted that the horizontal aperture correction signal generator which provides the signal C in the arrangement described in the aforesaid Patent Specification 1,293,315 is for simplicity replaced in the arrangement of Figure 1 by the high-pass filter 8 However, in both cases a signal processing operation is performed between the terminals A and D which corresponds to a given electric filter characteristic.

The aforesaid Patent Specification describes how the optical filter 1 should be made up of sectors which transmit the light L partly with reduced definition and partly with unreduced definition if the scene 4 contains a plurality of substantially saturated colours.

Using an R G B notation for the colour signals and the filter sectors, a notation Y=R+G+B for the luminance signal, and a dash over the corresponding symbol to denote an optical reduction in definition, the filter 1 comprises four groups of three sectors which each form a cycle, the three sectors of each group being Y; Y, R; and Y, G respectively Figure 3 shows part of the optical filter 1 containing one complete group During each field period Tv one of the said sectors rotates past the camera tube 2 Thus during each cycle of three field periods the signals Y;

Y+R; and Y+G are produced consecutively at the terminal A of Figure 1.

Figure 2 shows possible amplitude/frequency distributions of the frequency-restricted signals Y, R, G and B the non-restricted luminance signal Y, and the output C of the filter 8 It will be seen that the output of high-pass filter 8 will contain substantially zero contribution from the optically restricted signals R and G, so that only a high-frequency signal C=Cyg is produced thereat Using an accent notation, the result of the electrically performed frequency restriction is therefore Y'=Y-Cy Thus, the signals Y'; Y'+R; and Y'+G will appear successively at terminal D during the cycle of three field periods The matrix circuit 13 to which these signals are simultaneously applied performs the signal combinations:

(Y'+R) -Y'=R (Y'+G)-Y'=G ( 1) ( 2) Addition of ( 1) and ( 2) gives (R+G), and combination with Y' gives:

Y' (R+G) =Y' (Y-B) =B +Y'-Y (Because Y=R+G+B).

The signals R+ Cy, and B+(Y'-Y)+Cy thus appear at the output terminals 20, 21 and 22.

Figure 2 shows that the signals R+C and G+Cy, in contradistinction to the signal Y, do not necessarily have a flat amplitude/ frequency characteristic, whereas the signal B+Y'-Y+Cy does The reason for this is 110 1,406,889 1,406,889 the possible difference between the frequency characteristics of the signal Y' produced electrically by means of the signal Cy and the signal Y produced optically by means of the signals R and G If the signals Y, R, G, B and Y' (=R'=G'=B') had the same frequency characteristics the signals at the output terminals 20, 21 and 22 would have flat amplitude-frequency characteristics Figure 3 shows an optical filter 1 which enables the optical filter characteristics giving rise to the signals R and G to be made substantially equal to any desired electric filter characteristic, in particular to that giving rise to the signal Y', so that the equired equality of frequency characteristic can be attained.

Figure 4 shows that part of the optical filter 1 and its relationship to the camera tube 2 including the target 3 The camera tube 2 is shown symbolically as a glass face plate 23 which is internally coated with a transparent electrically conductive layer 24 which in turn is coated with a semiconductor layer 25 The layer 24, which is the signal plate, is connected via a load resistor (not shown) to an external voltage source (not shown).

Photo-leakage current resulting from the local illumination of the semiconductor layer 25 by the light L produces a potential image on the target 3 which comprises the layer 24 and Scanning the target 3 by an electron beam produces a voltage drop across the load resistor due to local neutralisation of the potential image The aforementioned picture signals are obtained from a capacitor connecting the junction of the signal plate and the resistor to the terminal A of Figure 1.

Before the optical filter 1 is described further, the requirements which its characteristic should satisfy will be discussed The curves of Figure 5 in which t denotes time and 1 denotes location, represent various quantities which vary in more or less the same way as a function of location or time Thus, the curve of Figure Sa when considered as a function of location I corresponds to a potential image on the target 3 produced by the light L This image is converted in tube 2 by means of electron beam scanning (which is assumed to be ideal) into an electric signal which is plotted as a function of time t so as to give the same curve Hence, the curve of Figure 5 a, also corresponds to a signal Y at the terminal A.

Figure 2 shows that it is desirable in the present example for the signal Y to be utilized in the pickup-display system up to a frequency of 3 M Hz This corresponds to a signal period of 200 ns so that if the signal is assumed to be a square-wave, the pulses in either direction will have a duration of 100 ns Owing to the finite frequency range such a pulse signal cannot have infinitely steep edges Figure 5 a shows the form which such a single pulse signal Y(A) having an amplitude a will take in practice The time of ns corresponds to an instantaneous amplitude of 2 a, this time being generally referred to as the "half-amplitude time".

The camera tube 2 will produce the described signal Y(A) of Figure 5 a if the scene 4 contains a spot of bright light which is imaged via the objective 5 onto the target 3 and converted into a local potential increase by the layer 25 (Figure 4) Owing to the fact that the imnage formation by the objective 5 will not be ideal and that charge will leak away from the potential image on the layer 25, the local potential increase will not correspond to a light spot but rather to a larger light patch The potential image is then scanned by the electron beam in the camnera tube 2 and owing to, amongst other factors, the finite diameter of the beam a picture signal is produced which corresponds to an even wider light patch This (optical) blurring which causes a light dot in a scene to become a light patch in a display corresponds to a restricted electrical frequency range in the pickup-display system It is possible to determine to what distance on the target 3 the half-amplitude time of 100 ns, designated by T,, of the signal Y(A) corresponds Assuming a line scan period of 54 /s and a line length of 8 1 mm on the target 3 of a miniaturised camera tube 2, the scanning velocity of the electron beam in the tube 2 will be equal to 8.1 prm/ns= 0 15 /m/ns.

Thus the signal half-amplitude time T,= 100 ns corresponds to a distance of lm on the target 3.

The signal Y(A) of Figure 5 a which is generated withl a frequency range up to 5 M Hz is processed in the circuit 7 of Figure 1, the filter 8 and the subtraction stage 9 producing the signal Y'=Y-C at the termninal D The signal Y'(D) is plotted as a function of time t in Figure 5 b for a Gaussian characteristic for the filter 8 (as a result of which the circuit 7 has a filter characteristic which corresponds to the well-known Gaussian curve; for a detailed description of Gaussian filters see "Handbook of Filter Synthesis" by A J Zverev, published by J Whiley and Sons, in particular pages 70-71 and 384385) In general such a filter has a loss-free impulse response in the time domain which is identical in shape to the signal shown, but has a half amplitude time To and an amplitude proportional to 1,406,889 This means that when the signal shown in Figure 5 a having an amplitude a and a half amplitude time T 1 is applied to the circuit 7 a signal having a half-amplitude time T 2 = V/T 2 +T'2 and an amplitude a T, appears at the output thereof The following relationship for the half-amplitude time To can be derived from the aforementioned pages 384 and 70:

0.588 T O = 8 (Ln 2)2 ( 3) 27 rfd B where f Id 3 is the 3 d B attenuation frequency for the filter From ( 3) 0.359 TO ( 4) f Md B If a 3 d B point of 450 K Hz is chosen for the signal Y', ( 4) gives:

0.359 To 796 ns.

450,000 The half-amplitude time T,= 100 ns of the input signal Y then results in a half-amplitude time T 2 of the output signal Y which is given by:

T 2 = TT 2 + T 2 = 800 ns The amplitude of the output signal Y' is equal to T 8 -a= 1/8 a.

T 2 This signal is shown in Figure 5 b as the signal Y'(D).

Comparison of the signal curves shown in Figures 5 ac and 5 b shows that the circuit 7 converts the 5 M Hz bandwidth input signal Y having an amplitude a and a half amplitude time of 100 ns into a 450 K Hz bandwidth output signal Y' having an amplitude 1/8 a and a half amplitude time of 800 ns To achieve a similar conversion by optical means would necessitate conversion of the potential increase on the target 3 having a peak value a and a half amplitude width of 15 gm shown in Figure 5 a by an optically introduced lack of definition into a potential increase having a peak value of 1/8 a and a half amplitude width of 800 X 15 = 120 iam (Figure 5 b) It has been found that the optically induced lack of definition has to be of a specific kind if it is to be matched to that introduced electrically Such a specific kind of optically induced decrease in definition can be obtained by means of the optical filter 1 shown in Figure 3 Figure 3 shows about one quarter of a circular disc which forms the optical filter 1 The disc comprises four groups of three equal sectors of a circle, the sectors of each group being denoted by Y; Y, R; and Y, G respectively Each sector is subdivided into two sub-sectors of different sizes Thus each sector of each group comprises a portion Y which transmits the light L from the scene 4 (Figure 1) without appreciably influencing it The other portions P and G of two of the sectors of the group each have a part made up from diffraction gratings, the remainder, which is equal in area, being opaque (Instead of providing the opague portion the entire sector Y could be provided with a neutral density filter However the design shown is normally cheaper and simpler, because it is easier to control the size of the opaque portion than the exact transmittance of the neutral density filter).

The sectors R and G each comprise six diffraction gratings z=l,, 6 which have differing spacings in the radial direction The spacings p in the gratings z= 1 is the largest, the spacings of the six gratings being in the ratio 1: 1/2: 1/3: 1/4: 1/5: 1/6: During each field period Ty one sector of a group rotates past the target 3 It is assumed that the area of incidence of the electron beam on the target 3 is initially slightly to the right of a point X on the target 3 and that the lines are scanned from right to left During the field period Tv in which the sector Y, G rotates past the point X this point X first receives the light L from the scene unimpeded through the sector Y, and subsequently through the successive diffraction gratings z of the sector G.

The light received during the field period Tv is integrated by photoconduction in the target 3 in known manner, the point X building up s 1,406,889 to a potential determined thereby When the electron beam is incident on the point X the charge thereat is neutralised, the integration of light starting anew when the next sector Y passes in front of point X It will be noted that the direction of the grating spacing substantially coincides with the line scan direction.

Before the action of the six diffraction gratings z in each of the sectors R and G is described, the operation of the diffraction gratings z= 1 having the largest spacing p will be described with reference to Figure 4.

In Figure 4 the optical filter 1 is provided with a diffraction grating 26 Grating 26 is a phase grating which is shown in cross-section and comprises strips of Si O 2 or silicon glass of depth q arranged on a glass plate 27 A colour filter layer 29 is sandwiched between the glass plate 27 and another glass plate 28.

If the grating is that indicated by the arrow in Figure 3 the layer 29 transmits only green light, whereas if the grating forms part of segment R in Figure 3, only red light will be transmitted The colour filter layer 29 need not form part of the optical filter 1, but may be disposed in front of or behind it so as to rotate with it in the path of the light L.

Although the diffraction grating 26 is described as a phase grating, a black-and-white grating may alternatively be used, although this will have the disadvantage that one half of the incident light L will be last therein.

It is known that the diffraction grating 26 will deflect some of the incident light L through angles a into certain directions given by:

n.A sin a,= ( 5) p where n= 0, 1, 2, and so on, and A is the wavelength of the light Figure 4 shows the angle a obtained for n= 1 Since only the cases n= 0 (undeflected light) and tl 1, i e the zero-order and first-order diffraction components, need be taken into account, Figure 4 will be described for the first-order component only.

With a small ( 5) becomes:

A sin a=a= ( 6) p and it will be seen from Figure 4 that then:

u tan a=a= ( 7) w ing to the first-order diffraction at a distance W from the grating 26.

From ( 6) and ( 7):

A u= W ( 8) p Because the light L will not be monochromatic but will contain a range of wavelengths, a mean wavelength A must be used in calculation Furthermore the light L passes through glass and air, so that the optical distance is equal to the real distance wv corrected for the index of refraction of glass, which here is 1 5.

If a wavelength of 0 54,,m is assumed for green light and O 62 /m for orange-red light, the mean wavelength A will be 0 58 1 jm.

Neglecting the depths of the grating 26 and the layer 29 and assuming thickness of 1 mm for each of the glass layers 27, 28 and 23 and an air gap of 3 mm between the filter 1 and the camera tube 2, we have 3 w-= 3 -5 mm 1.5 In will be assumed that the deflection distance u is 15 /tm, being the distance quoted for I in Figure 5 a However, other values may also be used.

Introducing the above values into ( 8) gives:

Aw 0 58 p=-= 5000 = 193 /em.

u 15 It has been assumed that the spacings p of the six diffraction gratings z are in the ratio 1, 1/2,, 1/6, i e that 193 Pz= /m.

z I: therefore follows that uz=z 15 j/m.

Figure Sc illustrates the result of the gratings passing in front of the point X When the diffraction grating z= 1 passes in front of the point X of the target 3 of Figure 3, the light L produces three potential increases having peak values Io, (zero order) and I,, (first order on either side of the zero order).

The diffraction grating z= 2 similarly produces zero order and first order potential increases having peak values I 02 and I 12, and an arbitrary diffraction grating z gives rise to peak values Io, and II.

The peak values I,0 all occur at the same point and after addition give a value I, The peak values I,, are each displaced by a distance 15 z /lm, and the corresponding potenwhere it is the deflection distance correspond1,406,889 tial increases which are discontinuous in space have an envelope denoted by R', G' The envelope R', G' is obtained by the integration of the light which is performed in the target 3 of the camera tube 2 over part of the field period Tv.

It will be seen from Figure 5 c that with the peak values Io, and I, assumed, the envelope R', G' is a good approximation to the curve of Figure 5 b which represents the signal Y', and can result in signals R and G for which R=R' and G=G' appearing at the terminal A Thus a decrease of definition which corresponds to the curve of Figure 5 b can be obtained optically Furthermore, as desired, this decrease of definition occurs only in the horizontal or line scan direction, since the line scan direction and the direction of the diffraction grating spacing substantially coincide.

The correct values of Ioz and I, can be selected, both for phase and black-and-white gratings by suitably choosing the widths ofthe gratings z as measured in the direction of rotation of the filter 1 In the filter 1 shown in Figure 3 the widths decrease with increasing z and hence each successive grating z moves past the point X in a shorter time, so that the corresponding values of Iz and Iz have smaller values Alternatively, each grating z could be provided with a separate neutral density filter.

However, adjustment of the areas thereof is simpler and results in more light being transmitted.

As compared with a black-and-white diffraction grating, a phase diffraction grating has the advantage that the depth of the strips be chosen at will and may be used to determine the values of Io, and I',, possibly in conjunction with the aforedescribed area selection.

Selection of the correct values of Ioz and IL by means of the strip depth of a phase grating will now be described.

The time axis of the Gaussian curve in Figure 5 b is divided into eight equal parts in each direction from its centre, i e from its maximum amplitude point Six parts are designated by z= 1, 2, 3, 4, 5, 6 If I is the sin 2 3: r 2 / \ 3 r height of the curve above the time axis we can write:

( 9) Calculating expression ( 9) for z= 1, 2, 6 gives:

11:12: I 12: I 4: I: I: I 1 Go 0.95: 0 82: 0 63: 0 46: 0 30: 0 18 ( 10) A diffraction grating z not only produces one of the first order components I 1, but also one of the zero order components Ioz As is shown in Figure 5 c the zero order components Io, are added together to give one component Io The component Io must, have the value 1 relative to the ratios given in ( 10) to satisfy the Gaussian curve and this determines the relationship between I,, and Ioz to be derived for each diffraction grating z.

Assuming Io =d IL for each grating z then we must have Io=Io+Io 2 + + Ioo= 1 and:

I 11 +I 12 + +I,= 3 34 (from ( 10)) Both relationships will be satisfied if 1 d=-= 0 3 3.34 Thus an approximately Gaussian curve will be obtained if:

Io,= O 3 Lz ( 11) for each diffraction grating.

If the diffraction grating 26 (Figure 4) is a phase grating, the relationship I,, = O 3 I,,L can be obtained for each diffraction grating z by suitably choosing the depth q of the strips of the grating This is because, if the strip depth q is of the order of the wavelength of the light, and the light L reaches the grating 26 with a plane wave front it can be shown that the light is diffracted into the zero and the various higher odd orders in the following intensity ratios (the even order components being zero):

sin:

2 f 2 sin W r 2 :and so on, where q p-= 2 ir radians X ( 12) p: ( 2 cos, 1,406,889 From this is follows that:

Ioz p cos I,, 4 ft sin 2 w 2 2 From ( 11) and ( 13):

f W 2 10 tan 2 i e.

2 4 3 3 = 141 = 0 39 times 2 radians ( 14) From ( 12) and ( 14):

q= O 39 A ( 15) The depth q calculated in ( 15) is the socalled optical depth which must be corrected when calculating the real thickness of the silicon glass of the strips, which has a refractive index of about 1 5 The real thickness q of the silicon glass is thus:

0.39 A 0 78 A 1.5-1 with A= O 58 mnn:

q= 0 45 {am.

It has been found that it is an advantage to use a phase grating because of the ease with which the desired light intensity distribution can be obtained by varying the strip depth The use of a black-and-white grating does not give this facility, it being necessary then to suitably choose the grating area or to vary the spacings of the various gratings.

Although approximation to a Gaussian curve has been described using six diffraction gratings having different spacings, a smaller number of gratings may be used if the approximation required is not so stringent.

The number of diffraction gratings required also depends upon the desired increase of the half amplitude width which in Figures 5 a and 5 c has been increased from 15 tzm to 120 pm If an enlargement to only 50 jam were desired, three diffraction gratings could be used, the orders being spaced by 10 Itm instead of by 15 anm.