GB1593531A - Scanning method and apparatus for imaging radiation - Google Patents

Description

(54) SCANNING METHOD AND APPARATUS FOR IMAGING RADIATION (71) We, SIRA INSTITUTE LIMITED, a British Company of South Hill, Chislehurst, Kent, BR7 5EH, 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 present invention relates to scanning method and apparatus for imaging radiation including a holographic lens.

The invention provides a scanning apparatus for scanning non-diffuse strip material comprising a source of monochromatic radiation, a scanner, a photodetector, and a holographic lens arranged such that the scanner and photodetector lie at conjugate positions but the path of the beam of radiation detected by the photodetector traverses an off-axis section of the lens.

Thus only part of the complete hologram is produced and utilised off-axis so that the spatial frequency of the pattern comprising the hologram falls to zero at no point within the area of hologram used. This prevents localised losses in focusing efficiency.

The source may be a laser, the scanner a rotatable multiple facetted mirror drum, the detector may comprise a photomultiplier and the radiation may reach the detector after reflection or transmission by the strip material.

Normally the pattern will be carried on a recording medium, but there is no need for a hologram to be permanent. For example, an acousto-optic deflector for laser beams is a hologram although the hologram only exists when there is a standing acoustical wave set up in the crystal which varies its refractive index.

Furthermore, such a hologram does not have to be acoustically based.

The hologram may be derived by, for example, a computer from an analysis of the mathematics involved but we prefer to derive the hologram optically.

We prefer to manufacture the hologram by scanning, that is to arrange during manufacture that adjacent parts of the recording medium are illuminated successively. This can be carried out effectively by providing two sources of radiation, the beams from which overlap at the recording medium, the overlapping area being moved across the surface of the medium to manufacture the hologram.

Preferably the scanning movement of the beam is a rotary movement, that is the angle of the beam to the axis is continuously varied and the means for causing this rotary movement may be in the form of a scanning means comprising a rotary mirror.

Preferred embodiments of the invention will now be described by way of example only and with reference to the accompanying diagrammatic drawings in which: Figure 1 shows the construction of hologram, Figure 2 shows the reconstruction of an image using the hologram of Figure 1, Figures 3A and 4A show front views and Figures 3B and 4B show side views of methods of reconstructing an image using a hologram constructed according to methods illustrated in Figures 3C and 4C respectively, Figure 5 is a typical apparatus for constructing a hologram used in the invention Figures 6, 7 and 8 are diagrams for use in the mathematical analysis of a hologram used in the invention, Figure 9 is a side view of a preferred apparatus incorporating a hologram of the present invention, Figure 10 is a front view of the apparatus of Figure 9, and, Figure 11 illustrates the portion of the hologram used.

The primary object of the present arrangement is to use a hologram to replace a conventional optical element such as a lens or mirror. The term "optical" is used in the Specification for convenience but, of course, the invention is not restricted to optical wavelengths. In particular, it is intended to use the holographic element in a scanning surface inspection system.

It should be understood that conventional optical elements and holographic optical elements are not generally interchangeable in the sense that a holographic lens or mirror can simply replace a conventional optical lens or mirror. However, if the system can be modified or arranged so that holographic optical elements can be utilised they are generally found to be lighter than their conventional counterparts (this is particularly true for lenses) since they can be of thin flexible material and the construction of the hologram can be modified to allow it to be used for the scanning of non-flat surfaces.

It has also been found that in scanning systems the aberrations introduced by conventional optical elements limit the resolution which can be obtained. The use of holographic optical elements alleviate this restriction without incurring an excessive increase in cost.

In accordance with Figure 1 which shows the method of construction of a hologram, the.hologram 10 is made using a reference source 11, which produces a diverging spherical wave 12, and a converging (spherical wave) construction beam 13 coherent with the reference source 11 which forms a virtual object 14, the reference source 11 and the virtual object 14 being on opposite sides of the hologram plate 10 at equal distances a along an axis 15 normal to the hologram.

Thus the hologram 10 is formed by interference between the diverging spherical wave 12 and a converging construction beam 13.

Referring to Figure 2 the reconstruction is made, in this particular case, by using radiation of the same wavelength as that used during the formation of the hologram 10 and with an aperture stop 16 at the same position relative to the hologram as the reference source 11. As is clear from Figure 2, the reconstruction radiation is in the form of a monochromatic coherent collimated beam 17 and it will be seen that the image 18 is formed on a plane surface 19 parallel to the hologram 10 at a distance a 2 from it. In this instance, therefore, the image 18 produced is not a reproduction of the image of the object source as is utilised in conventional holography. A different image is produced by the use of the collimated beam 17 and as is clear from Figure 2, when the collimated beam 17 is not normal to the hologram 10 (that is, not along the axis 15) the image 18 is formed off the axis 15.

This image 18 is free from astigmatism and the system provides a flat field (i.e. plane surface 19) for all values of scanning angle 0 so that by varying the scanning angle 0 (that is by rotating the collimated beam 17 about the aperture stop 16,) the image 18 can be made to move from side to side along the plane surface 19.

If a reflective planar object 22 is mounted coincident with the plane surface 19, the light reflected from the object 22 is reflected back to the position 23 (i.e. the point at which the axis 15 meets the hologram 10) for all values ofO and similarly if a planar light transmitting object is placed at the plane surface 19 then the beam will pass through a position 25 corresponding to the position of the virtual object 14 in Figure 1.

As is clear from the Figure, the aperture stop 16 and the positions 23 or 25 are conjugate with respect to the holographic lens 10 at least in the plane of Figure 2.

A photodetector 24 may therefore be placed at the position 23. It is necessary that this detector 24 occupy an area the size of the collimated beam 17 since the reflected beam is divergent at this point.

The undiffracted light of the zero order is reflected out of the system. The conjugate image beam (first order) is also lost from the system. Higher orders are not reflected back to the detector as they strike the specimen at angles approximately equal to 2S, 30 etc.

It will be understood that the reconstruction collimated beam 17 may be of a broad spectrum of radiation but we prefer it to be monochromatic.

Other optical arrangements are illustrated in Figures 3A, 3B and 3C and Figures 4A and 4B.

Figure 3C shows an alternative optical arrangement for the construction of a hologram 10' using a reference source 11' which produces a diverging spherical wave 12' and a collimated construction beam 13' coherent with the reference source 11'. It will be noted that the hologram 10' is curved. The hologram 10' is formed by interference between the diverging spherical wave 12' and the beam 13'.

The hologram 10' produced according to Figure 3C may be utilised as illustrated in Figure 3A, in which Figure 3A shows a view corresponding to Figure 2 and is in the same plane as Figure 3C. The reconstruction is made by using radiation of the same wavelength as that used during the formation of hologram 10' with an aperture stop 16' at the same position relative to the hologram 10' as the reference source 11'. The reconstruction radiation is in the form of a monochromatic coherent collimated beam 17' and it will be seen that the image 18' is formed on a plane surface 19' at which is mounted object 22' to be inspected.

As before the beam 17' may be scanned back and forth in the plane of Figure 3A by providing a scanning apparatus at the aperture stop 16'. In practice if the scanning apparatus is a mirror drum then the mirror drum may if necessary provide the aperture stop 16'.

From Figure 3B, it will be seen that the beam 17' is arranged so as not to pass through the axis of the hologram 10' but is offset from it in the plane of Figure 3B which is at right angles to the plane of Figure 3A. This may be more clearly understood by reference to Figure 11 which shows a plan view of the hologram 10.

As has been described before it is preferred not to use the portion of the hologram where the spatial frequency falls to zero and so we therefore use a strip of hologram not incorporating the axis. We could utilise the strip 10A which extends radially with respect to the axis of the hologram 10 but in practice we prefer to use the strip 10B which is generally tangential to a circle centered on the axis of the hologram 10. It will be understood, therefore, that the aperture stop 16' (which forms the source of the coherent monochromatic radiation) will be on the axis of the hologram 10 and in the plane of Figure 3B the beam of radiation 17' will be directed away from that axis so as to utilise the strip 10B of the hologram and thus the detector 24' will be of course off the axis of the hologram.

Figures 3A and 3B also illustrate another feature of this arrangement. It will be clear that the focusing in the two planes of Figures 3A and 3B is different, that is, the collimated beam from aperture 16' in the plane of Figure 3A is brought to a focus on the plane surface 19' whereas in Figure 3B the beam in this plane is brought to a focus at point 25' between the hologram 10 and the detector 24'.

Although not illustrated, a similar arrangement is true in Figure 2, that is, the focusing in the plane of Figure 2 and a plane at right angles thereto are different.

A similar arrangement is illustrated in Figures 4A, B and C, the similarities and differences being readily apparent. In this case, as in the case of Figure 2, the aperture 16" and the photodetector 24" are both on the axis of the hologram although once again an off-axis portion of the hologram such as the portion 10B is utilised. Further description of Figure 4A, B and C is not deemed necessary in view of the description of Figures 3A, B and C.

As already described with reference to Figure 11 we wish to avoid the use of the centre of the hologram that is, the area adjacent the axis as the focusing properties of the hologram are poor in that area. We therefore wish to construct a strip type hologram of an area corresponding to the area 10B shown in Figure 11, and the method of constructing such a strip type hologram is shown in Figure 5. In Figure 5, the recording plate which is to carry the hologram pattern is illustrated at 30 and a beam 31 of radiation from a laser is passed through a rotatable parallel sided optical block 32 to a beam splitter 33, part of the beam then passing on to a further rotatable optical block 34 and then to two mirrors 35, 36 where it is directed into a microscope object glass 37 to produce a beam 38 of radiation. The other beam from the beam splitter 33 is reflected from mirror 39 to an object glass 40 which similarily forms a diverging beam 41. Both beams are diverging from foci just in front of their respective object glasses on the optic axis.

The block 32 scans the light across the pupil of the object glass 40 and thereby causes changes in the scanning angle 0, of the beam 41 from the object glass 40 so as to cause the beam 41 to move across the plate 30. Similarly, the optical block 34 will cause changes in the scanning angle 02 of the beam 38. Clearly if the two beams 38, 41 are to move in unison and overlap at the hologram plate as is illustrated some additional compensation will have to be made in the scanning angle 02 relative to O and this is provided by the optical block 34. This ensures that the two beams 38, 41 overlap at all times.

In this way by scanning the beams across the hologram plate during its manufacture rather than illuminating the whole of the hologram simdltaneously, the exposure time for each element Qf the hologram is reduced and it provides a method for uniformly illuminating a long narrow strip of the hologram without the need for cylindrical or other beam distorting object. As mentioned above. In practice, it is intended that the hologram should only be in the form of a strip the longitudinal axis of which is vertical in Figure 5.

During the construction process illustrated in Figure 5, the beam from the laser is passed to the pupil of the object glasses 37 and 40 slightly to one side of the axis. For example, in Figure 5 the beam may be moved across the pupil of the object glass in a line parallel to the plane of the paper but slightly above that plane.

In that case, the strip hologram 30 produced will be a strip slightly behind the plane of Figure 5, i.e. strip 10B of Figure 11.

One of the problems with holograms is that it would be preferable to use a laser of relatively short wavelength during construction of the hologram since the shorter wavelength lasers are generally more powerful and one may use a wider range of holographic recording -materiai. However, it is preferred not to use such shorter wavelength lasers in reconstruction since they tend to be expensive to buy and run. It is therefore preferred during reconstruction to use a He-Ne laser operating at 633 nm.

The change in wavelength between construction and reconstruction permits the convergence or divergence of the two constructing beams to be altered. For a sufficiently large wavelength ratio both constructing beams can be divergent instead of one being convergent and this greatly simplifies the procedure for construction of the hologram.

In the present instance, any aberrations caused by the use of different wavelengths can be corrected by introducing a further optical element into one of the construction beams or by bending the hologram (it is assumed that the hologram would normally be used flat although this is not necessary).

The holographic lens utilised in the present embodiment is essentially a holographically generated diffraction grating with a line spacing which varies from point to point. We can investigate mathematically the possibilities of using different wavelengths for construction and reconstruction as follows and with reference to Figure 6: Construction wavelength (wavelength of manufacture) Reconstruction wavelength (wavelength of use) Wavelength ratio (AJA1) Pupil conjugate distance in use i.e. distance from pupil P to hologram H L1 distance from hologram H to image I L2 Source points S" S2 to hologram distance in construction A, B Pupil radius at hologram r Focal length during reconstruction f Focal length during construction For the lens to have the correct power i.e. to deviate the beam through the correct angle we must have (Figure 6): 1 1 1 = , L1 L2 f and, 1 1 1 A B f' but 1 α/f = f' so:- 1111111 - - - - - - - = - ) (I) L1 L2 f af' or A B For our particular use L2 will be equal to L1 and on the opposite side of the hologram .. L2=-L1 and equation (1) reduces to: 2.1 1 1 = ( - ) (2) L α A B For zero primary (third-order) pupil spherical aberration we also must have: 2 1 1 1 - ( - )=0 (3) L3 a A3 B3 (which will be derived later) Now using (2) and (3) to eliminate A the resulting quadratic equation solved for B/L.

B2 B (1-4α) -6α -3=0 (4) L L B + 3α # 3#(1-α) = (5) L (1-4α) For a > 0.5, B/L1 is negative. It is still necessary to employ a converging beam for construction unless a UV laser is used for construction and/or an IR laser for reconstruction if the primary correction is required for two constructing beams diverging on to a flat plate from point sources. However, we prefer to use a diverging beam.

If instead we select a value of a which will be 488 Jargon i.e. =0.77 633 helium neon then the residual primary wavefront aberration can be computed as follows (Figure 6): In general d(Sin #L1+Sin #L2)=m#1 for mth order diffraction where d is the fringe spacing also d(Sin #A-Sin #B)=m#2 #1 Sin #L1+Sin #L2= (Sin #A-Sin #B) #2 For the paraxial case (Sin #=#=Tan 0)

which is equation 2 Outside the paraxial region Sin #=#-#3/31+#5/5!------ Tan #=#+#3/3+2 #5/15±----- Restricting these to the first two terms only we get Tan # Sin #=Tan # 2 r r3 L 2L3 Therefore

r r r r 1 r r r r - + - = - - + L1 2L1 L2 2L2 α A A B B and subtracting Equation 1 gives:

2 1 1 1 = # ~ # L3 α A B which is Equation 3.

To calculate the spherical aberration refer to Figure 7. Draw circles #i passing through the point r distant from the axis. These intercept the axis at distance S1',S2', S' and S" from the hologram. For perfect correction away from the paraxial region we must have.

S'-S"=a(S1+S2)=2aS for L1=L2 Now (L+S)=L+r S=(L+r)-L (A+S')=A+r S'=(A+r)-A (B+S")=B+r S"=(B+r)-B and the residual wavefront aberration will be (S'-S")-2aS. Expanding in powers of r we get:

r r4 (S' - S") - 2αS - A 1 + - + .... 2A 8A4

r r4 r r4 A - B 1 + - + .... + B - 2αL 1 + - ... + 2αL 2B 8B4 2L 8L4 But 1/A=2/Lα+1/B and eliminating A gives

8α - 2α 12α 6α - r4 # + + L LB LB

r4 = - α/4 (4α-1) + 6α L/B + 3 (L/B) L which for a=488/633

r4 r4 -0.193 1.377 + 4.626 L/B + 3 (L/B) # 0.5 L L This is the residual spherical aberration but we can correct it by inserting an optical component during construction with an opposite amount of spherical aberration to this aberration.

The primary spherical aberration can also be corrected without the aid of correcting optics by curving the hologram during manufacture. This gives an extra degree of freedom (the radius of curvature) R of the hologram which is sufficient to provide an exact correction for any wavelength ratio #1. R can be calculated with reference to Figure 8. In Figure 8; d=R# (d is length along the surface of the hologram) h=R Sin # a=R(1-Cos #) RB=h+(LB-a) RA=h2+(LAa)2 Wave front separation W=(RA-LA)-(RB-LB) W=(h+(LA-a))-(H+(LB-a))-LA+LB =(R Sin#LA-2RLa(1-Cos #)+R(1-2 Cos#+Cos#)) -(RSin#+LB-2RLB(1-Cos#)+R(1-2Cos#+Cos#))-LA+LB =(2R(1-Cos#)-2RLA(1-Cos#)+LA) -(2R(1-Cos#)-2RLB(1-Cos#)+LB)-LA+LB =(LA+2RLA(1-Cos#)(R/LA-1))-(LB+2RLB(1-Cos#)(R/LB-1))-LA+L

2R R = LA # 1 + (1 - Cos #) - 1 - 1 # LA LA 2R R - LB # 1 + (1 - Cos #) - 1 -1 # LB LB W is now expanded as a power series by the binomial theorem

R R R W = R(1 - Cos #) - 1 - (1 - Cos #) - 1 LA LA LA R R R4 R + (1 - Cos #) - 1 - 5/8 (1 - Cos #)4 - 1 4 + LA LA LA LA terms in higher powers of R

R R R - R (1- Cos #) - 1 + (1 - Cos #) - 1 LB LB LB

R R R4 R - (1-Cos #) - 1 + 5/8 (1 - Cos #)4 - 1 4 + LB LB LB LB terms in higher powers of R Expanding (1-Cos#)n as a power series we get

# #4 1 1 R4 # #4 1 1 W=R - + .... - - - + .... - 2! 4! LA R LA 2! 4! LA R R6 # #4 1 + - + .... - 1/R + terms in higher powers of R LA 2! 4! LA # #4 1 R4 # #4 1 - R - + .... - 1/R + - + .... - 1/R 2! 4! LB LB 2! 4! LB R6 # #4 1 - - + .... - 1/R + terms in higher powers of R LB 2! 4! LB 1 1 1 1 = d - d/R + d/R4 - .... - 1/R 2! 4! 6! LA d4 1 1 1 1 - - d/R + d/R4 - .... - LA 2! 4! 6! LA R d6 1 1 1 1 + - d/R + d/R4 - .... - 1/R LA 2! 4! 6! LA 5 10 15 + terms in higher powers of d

1 1 1 - d - d/R + d/R4 - .... - 1/R 2! 4! 6! LB d4 1 1 1 + - d/R + d/R4 - .... - 1/R LB 2! 4! 6! LB d 1 1 1 1 - - d/R + d/R4 -.... - LB 2! 4! 6! LB 1 1 1 1 1 = d - d/R + d/R4 - .... 2! 4! 6! LA LB d4 1 1 1 1 1 1 1 1 - - d/R + d/R4 -.... # - 1/R - - 1/R # 2 2! 4! 6! LA LA LB LB d6 1 1 1 1 1 1 1 + - d/R + d/R4 -.... # - 1/R - - 1/R # 2 2! 4! 6! LA LA LB LB | + terms in higher powers of d =n2#2 For reconstruction R##LA=-LB=L d d4 d6 W= - + -...=n1#1 L 4L 8L5 For a first order correction set n,=n2

d d 1 1 #2 = - = α L#1 2#2 LA LB #1 2 1 1 1 L α LA LB For a third-order correction (primary spherical aberration)

1 d4 1 1 1 1 1 1 1 1 1 = d4 # - + 1/8 - - - # #1 4L #2 4! R LA LB LA LA R LB LB R 5 10 15

a a 1 1 2 1 1 2 1 = + - + - + 4L 12RL 8 LA LAR LAR LB LBR LBR α 2α 1 1 1 4α 1 1 2α = + 1/8 # + + - + + # 12RL L LA LALB LB LR LA LB LR 1 1 1 1 1 1 1 1 = + + + - 2/R + + L 3R LA LALB LB R LA LB R

Claims (20)

WHAT WE CLAIM IS:

1. A scanning apparatus for scanning non-diffuse strip material comprising a source of monochromatic radiation, a scanner, a photodetector, and holographic lens arranged such that the scanner and photodetector lie at conjugate positions but the path of the beam of radiation detected by the photodetector traverses an off-axis section of the lens.

2. Apparatus as claimed in claim 1 in which the source is a laser.

3. Apparatus as claimed in claims 1 or 2 in which the scanner is a rotatable multiple facetted mirror drum.

4. Apparatus as claimed in any of claims 1 to 3 in which the detector comprises a photomultiplier.

5. Apparatus as claimed in any of claims 1 to 4 in which the components are arranged such that the radiation reaches the detector after reflection by the strip material.

6. Apparatus as claimed in any of claims 1 to 4 in which the components are arranged such that the radiation reaches the detector after transmission by the strip material.

7. Apparatus as claimed in any of claims 1 to 6 in which the holographic lens comprises a pattern carried on a recording medium.

8. Apparatus as claimed in claim 7 in which the pattern comprising the holographic lens is computer derived.

9. Apparatus as claimed in claim 7 in which the pattern comprising the holographic lens is derived optically.

10. Apparatus as claimed in claim 1 substantially as hereinbefore described with reference to the accompanying drawings.

11. A method of scanning non-diffuse strip material comprising providing a source of monochromatic radiation, scanning the radiation across the strip material by means of a scanner, detecting the radiation from the strip material by means of a photodetector, the radiation being focused by a holographic lens arranged such that the scanner and the detector lie at conjugate positions, the axis of the holographic lens being arranged away from the path of the beam of radiation detected.

12. A method as claimed in claim 11 in which the radiation is reflected by the strip material.

13. A method as claimed in claim 10 in which the radiation is transmitted by the strip material.

14. A method as claimed in any of claims 11 to 13 in which the holographic lens comprises a pattern carried on a recording medium.

15. A method as claimed in claim 14 in which the pattern forming the hologram is derived by a computer.

16. A method as claimed in claim 14 in which the pattern forming the hologram is derived optically.

17. A method as claimed in claim 16 in which the hologram is produced by scanning by two interfering light beams, adjacent parts of the recording medium being illuminated successively.

18. A method as claimed in claim 17 in which the two interfering beams of radiation are provided by two sources of radiation, the beams from which overlap at the recording medium, the overlapping area being moved across the surface of the medium to manufacture the hologram.

19. A method as claimed in claim 18 in which the scanning movement of the overlapping area is a rotary movement so that the angle of the beam to the axis is continuously varied.

20. A method as claimed in claim 11 for scanning non-diffuse strip material substantially as hereinbefore described.