WO2013124648A1

WO2013124648A1 - Grinding/polishing machine for aspheric optical surfaces using a template

Info

Publication number: WO2013124648A1
Application number: PCT/GB2013/050408
Authority: WO
Inventors: Roderick V. WILLSTROP
Original assignee: Cambridge Enterprise Limited
Priority date: 2012-02-21
Filing date: 2013-02-20
Publication date: 2013-08-29
Also published as: GB201202896D0

Abstract

The aspheric optical surface grinding machine (200) has a frame defining an optical axis (204) of an optical element to be provided with an aspheric optical surface (218a); a template (216) with a curved template surface (216a) representing a desired aspheric surface (218a) of the optical element; and at least one rocking bar (202). The rocking bar (202) is mounted on the frame with a fiducial surface (202a) arranged to bear against the template surface (216a), such that as said rocking bar (202) rocks the fiducial surface (202a) remains in contact with and rolls over the template surface (216a) and a point of contact of said fiducial surface (202a) with said template surface (216a) moves along said template surface (216a). The fiducial surface (202a) defines substantially a tangent to the template surface (216a) at the moving point of contact, and is linear and rigid in a direction of the tangent. A tool support (206) is attached to the rocking bar (202), to support a tool (210) for shaping the optical surface (218a). The tool support (206) has an axis (300) located in a plane parallel to the plane of the rocking bar (202) and containing the optical axis (204) and is directed substantially parallel to the tangent. The grinding machine (200) also includes a system to hold the rocking bar (202) to inhibit the bar (202) from slipping longitudinally along a direction of the tangent.

Description

Grinding/polishing machine

FIELD OF THE INVENTION This invention relates to apparatus for grinding optical surfaces, in particular aspheric optical surfaces.

BACKGROUND TO THE INVENTION Spherical optical surfaces can be mass-produced, some techniques being able to produce surface tolerances of a fraction of the wavelength of visible light. Aspheric surfaces may be mass-produced by moulding, which usually results in a quality which is suitable for use as condenser lenses, but little else. Very high quality aspheric mirrors or lenses may be shaped on a precision lathe, using a single-point diamond tool under real-time computer control, with the position of the tool monitored by (at least) two laser interferometers. The high capital and running costs of such high-tech equipment means that their products cannot be expected to be, or to become in future, as cheap as spherical-surfaced optics. The surface finish obtained by diamond turning is smooth enough for use in the infra-red spectrum, but for use at visible wavelengths the surface must be polished.

Optical design programmes such as ZEMAX™ commonly produce designs requiring aspheric surfaces and quicker/cheaper techniques for fabricating such surfaces are desirable. A particular problem faced by the inventor is fabrication of aspheric lenses for illumination of the Ante-Chapel of King's College, Cambridge, UK, background to which can be found in, "Null Test for a Deeply Aspheric Lens", R. Willstrop, Applied Optics, Vol 50 (25), pages 4977-81.

Historically grinding machines have been used to fabricate aspheric optical surfaces as described, for example, in GB1 , 314,824; US3,535,825 and, more particularly, GB593.759 Burch. (The Burch machine is also described in, 'Prism and Lens Making', F. Twyman, second edition, Hilger and Watts Limited, 1952, Figures 154, 155, PP360- 363). Further background material can be found in 'Aspheric Optics', E. Heynacher, Phys. Technol., Vol 10, 1979, PP124-131 in particular at page 126 referring to Figure 3. Further general background material can be found in, 'Amateur Telescope Making' Book 3, Scientific American, 1953, at page 432 (Figure 2).

The Burch machine appears to represent the closest prior art. This describes a machine in which a rod 29 rolls along a cam surface 30a (Figures 1-3 and page 9) at the same time as a grinding or polishing pad 5, 6 is moved over the surface of lens 1. In the Figures broadly speaking the portion of the apparatus on table 12 moves the grinding pad back and forth over the lens with adjustable travel. Broadly speaking the manner in which the Burch machine operates is similar to historical practices for lens/mirror grinding - the grinding pad floats on the lens surface and where the grinding takes place can be adjusted. A user employs the mechanism to grind approximately the aspheric surface; the lens is then removed, the surface figure checked, and then the machine manually re-adjusted so as gradually to approach the desired shape. It is inherent in the operation of the Burch machine that rod 29 is allowed to slip along the surface of cam 30, and that the grinding/polishing pad floats on the lens surface. The advantage provided by the Burch mechanism is not the automatic shaping of an aspheric surface but rather the angle-control illustrated in Figure 155 of Twyman's book (imagining the surfaces depicted there as wrapped across the surface of a lens/mirror). Quoting from the Twyman book (and noting from the footnote that the description here appears to have come from Dr Burch himself), 'thus although angle-control does not automatically generate the desired shape, it enhances the tendency of the machine to make smooth approximations to the desired shape'. The approach described in the Heynacher article involves a 'permanently tensioned steel band' (caption to Figure 3), and this introduces practical difficulties, inter alia, in applying the necessary tension. In practice the Heynacher approach does not work well.

SUMMARY OF THE INVENTION

According to the present invention there is therefore provided an aspheric optical surface grinding machine, the machine comprising, a frame, said frame defining an optical axis of an optical element to be provided with an aspheric optical surface; a template mounted on said frame and having a curved template surface representing a desired aspheric surface of said optical element; at least one rocking bar mounted on said frame and able to rock in a first plane, wherein said rocking bar has a fiducial surface arranged to bear against said template surface, such that as said rocking bar rocks said fiducial surface remains in contact with and rolls over said template surface and a point of contact of said fiducial surface with said template surface moves along said template surface, wherein said fiducial surface defines substantially a tangent to said template surface at said moving point of contact and is linear and rigid in a direction of said tangent; a tool support, attached to said rocking bar, to support a tool for shaping said optical surface, wherein said tool support has an axis located in a plane parallel to said first plane and containing said optical axis and is directed substantially parallel to said tangent; and a system to hold said rocking bar to inhibit said rocking bar from slipping longitudinally along a direction of said tangent. In general the optical element will be a lens or mirror. Embodiments of the machine address the problems described in the introduction and provide apparatus which will automatically generate a required aspheric surface. Moreover this can be done faster than by traditional optical working techniques, and more cheaply than by employing a lathe with a single-diamond tool. Embodiments of the apparatus can be used to grind both convex and concave surfaces on lenses and mirrors, and can produce a very high quality surface finish. In this specification, therefore, references to 'grinding' optionally include polishing.

The system to hold the rocking bar in place longitudinally in some preferred embodiments comprises a flexible strap attached between the rocking bar and the curved template or between the rocking bar and the frame. Preferably the strap is attached to the curved template beyond the limit of contact with the rocking bar (and thus preferably the template surface extends far enough to allow the strap to be fixed in this way. Preferably the system also includes a tensioning means to tension the strap, preferably pulling substantially along the rocking bar and tangentially to the template surface (herein also called the cam surface of a 'cam' template). In embodiments the means for tensioning a strap comprises an elastic element under tension, for example a spring or elastic strip or band. In embodiments the flexible strap may be a metal strap, for example also of a spring-type material such as phosphor-bronze. Alternative techniques which may be employed for tensioning the strap include (but are not limited to) a weight and a cord passing over a pulley and similar gravity-tensioning arrangements. Because the strap has a finite thickness in embodiments the rigid, linear surface of the rocking bar will not be precisely aligned along a tangent to the template surface. However since the strap is preferably relatively thin the displacement will only be small and will have a negligible effect on the shape of the optical surface (and optionally the axis of the grinding tool may be displaced from the plane of the fiducial surfaces of the rocking bars by an amount equal to the thickness of the flexible strap). In one preferred embodiment the mechanism for tensioning the strap comprises a pivoting arm with a tensioned elastic element coupling the arm to the rocking bar. Preferably the pivot is located longitudinally (as defined by the optical axis) between limits of contact of the rocking bar on the template surface. This ensures that any variation of the tension in the flexible strip is kept to a minimum, and so also minimises any elastic deformation (i.e. stretching) of the flexible strip. In preferred embodiments the pivot is located at approximately a mean centre of curvature of the optical surface. Preferably the hinge is also located in a (horizontal) plane comprising the optical axis (perpendicular to the first, vertical plane). In practice some tolerance of the pivot position is acceptable (and the pivot may be below the optical axis in the horizontal plane); optionally the pivot may be located beyond the further limit of contact of the rocking bar with the template surface.

In some preferred embodiments the tool support comprises a stop to limit travel of the tool along the line of the fiducial surface of the rocking bar, and may then also include bias means, such as a spring, to urge the tool towards this stop. This is advantageous because unlike the 'grind and test' approach of Burch this effectively defines the surface so that grinding is, effectively, just a case of feeding the optical surface towards the tool and grinding off as much as desired/needed - the desired shape may be generated automatically. This is particularly useful where a surface departs substantially from a spherical surface and/or a significant amount of glass is to be removed.

In some preferred embodiments a rocking bar may also be provided with a rocking bar stop to inhibit the bar/tool from moving beyond the optical axis - that is to keep the axis of the tool support to one side of the optical axis. In preferred embodiments a pair of rocking bars is provided, one to either side of the optical axis, thus defining a yoke. Then each rocking bar may be provided with a respective template and template surface. The tool support may then be provided on a cross-member of the yoke, for example comprising a mount for a tool, preferably including the previously described stop and bias means. This arrangement helps to provide increased rigidity. The tool may be incorporated into the machine or, more preferably, may be exchangeable. In one preferred implementation the tool is a rotating tool with an axis of rotation aligned substantially parallel to the tangent/fiducial surface of the rocking bar. In embodiments the tool may rotate at a high speed, for example greater than SOOrpm or lOOOrpm.

As previously mentioned, some preferred embodiments include a reciprocating drive for the rocking bar, for example a motor driving a crank. Preferably the apparatus includes a carriage, mechanically coupled to the frame, to support the optical element (lens or mirror) whose surface is to be ground/polished. Preferably the machine/carriage includes a linear feed for the optical element; this may be (motor) driven and/or manually operated, but preferably is under manual control. Preferably the carriage providing the linear feed comprises a motor driven shaft to rotate the optical element, for example at less than 100rpm. In one embodiment the linear feed comprises a moveable feed stop, for example comprising a micrometer screw, and bias means such as a spring to bias the optical element, more particularly the carriage/shaft on which it is mounted, towards this adjustable feed. Embodiments of the machine may be configured to grind either or both of a convex optical surface and a concave optical surface. In the case of a convex surface the face of the tool is directed inwards towards the yoke/template surfaces; for a concave surface the tool is directed away from the rocking bar arms of the yoke and away from the template surfaces (in both cases, however, still be aligned parallel to the rocking bar/tangent to the template surface). When grinding a concave surface the tool may be provided on an extension portion of the cross-member of the yoke to facilitate the tool grinding in the depressed central region of the concave surface. The skilled person will appreciate that the ground/polished surface may be the surface of either a lens or a mirror or, potentially some other optical component. The template surface representing the desired aspheric surface of the optical element in embodiments comprises an evolute of the aspheric surface (that is, the locus of its centres of curvature). Conceptually this can be generated by generating a normal to the desired surface at a succession of points on the surface, the envelope of these normals defining the surface of the template. In practice the shape of this surface can straightforwardly be generated from a power series describing the profile of the desired aspheric surface, using a computer program (or a package such as MathCAD™ or athematica™). In preferred embodiments of the machine the template is detachable so that a user- template may be defined and fabricated, for example by CNC (Computer Numerically Controlled) machining and then attached to the machine to grind a desired aspheric surface.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other aspects of the invention will now be further described, by way of example only, with reference to the accompanying figures, in which:

Figure 1 illustrates the relationship between an aspheric surface and the evolute of the surface;

Figures 2a to 2c show, respectively, side and plan views of an embodiment of an aspheric optical surface grinding machine according to an embodiment of the invention, and details of a tensioning arrangement for the machine;

Figure 3 shows details of a tool support for the machine of Figure 2; Figure 4 shows a schematic illustration of a lens/mirror carriage for the machine of Figure 2;

Figure 5 illustrates an example of a yoke for grinding a concave mirror/lens surface for use with the machine of Figure 2; and Figures 6a and 6b show, respectively, side and plan views of a variant of the tensioning arrangement for the machine of Figure 2.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Referring to Figure 1 , which is taken from US3,535,825, this schematically illustrates the relationship between an aspheric curve A'BA and an evolute of the curve, CF. The evolute is constructed from the envelope of the normals to curve A'BA, as schematically illustrated by the normals at points 1 , 2, 3, 4; these define tangents to the evolute CF. Evolute CF is the locus of the centres of curvature of curve A'BA. In the case of a lens/mirror curve A'BA represents a cross-section through a surface having rotational symmetry about optical axis OB.

Referring now to Figure 2, this shows side and plan views of a schematic illustration of an aspheric optical surface grinding machine 200 according to an embodiment of the invention. In figure 2, mechanical details of the frame of the machine are omitted for clarity.

A rocking bar 202 is provided on each side of the optical axis of the lens 204 (which is aligned with a spindle mounting the lens, as described later). The two rocking bars are joined by a cross member 206 to form a yoke 208. The yoke 208 carries a tool 210 (only schematically illustrated in figure 2) mounted on a tool support formed by cross- member 206. A thin, flat, flexible spring 212, for example of phosphor-bronze is provided for each rocking bar (only 1 is shown in Figure 2). This spring is attached to the rocking bar by an attachment 214a at one end, and to a template 216 by an attachment 214b at the other end. These attachments are outside the range limits of the points of contact between the template and rocking bar, as shown.

The template 216 has a curved surface 216a defining an evolute of a desired aspheric surface 218a of, in the illustrated example, lens 218. (In Figure 2a the aspheric surface is indicated by a solid line and a spherical surface it intersects is indicated by a dashed line). In embodiments the template 216 is removeably attached to the frame of the machine (not shown), for example by bolts, to facilitate the provision of different template 'cam' surfaces to define the desired optical surface - which may be, for example, elliptical, paraboloid hyperboloid, or some other shape. The shape of the curved template surface may be determined, for example, from a power series that describes the profile of the desired aspheric 218a. The skilled person would appreciate that this is a matter of routine mathematics/programming; an example program to determine the guiding cam profile is given later.

In embodiments the rocking bars 202 comprise a pair of flat metal bars, a lower face of each bar defining a fiducial surface which (apart from the thickness of spring 212) defines a tangent to the template surface 216a. In operation the lower face 202a of each bar rests and 'rolls' on the template surface 216a without slipping. To facilitate this the springs 2 2 are maintained in tension (to prevent buckling) by a convenient means. Figures 2b and 2c illustrate a preferred technique for maintaining the springs or straps 212 in tension: a rod or tensioning arm 220 is provided for each rocking bar, hinged or pivoted at a point 222, preferably on the optical axis 204, preferably between the limits of contact of the rocking bar on the template or cam surface, more preferably at substantially the mean centre of curvature of the optical surface 218a. At the other end of rod 220 a (coil) spring 224 has a point of attachment 226 to the rod and a point of attachment 228 to the rocking bar. This arrangement allows rods 220 to hinge and move together with the up and down motion of rocking bars 202 whilst maintaining springs 212 in tension. If the springs 212 exhibit a flat design, they may separate from the rocking bar 202 upon relaxation due to a small distortion. Hence, preferably the springs 212 maintain a slight residual curvature when they are relaxed, with the direction of the curvature being the same as the direction of the curvature of the cam. This allows for continual contact between the springs 212 and the cam as well as the springs 212 and the rocking bar 202, respectively. As previously mentioned, the lower, fiducial, surface 202a of rocking bar 202 defines a tangent to the curved template surface 216a. Preferably the rocking bars 202/yoke 208 is driven, for example by a motor and crank combination, such that it has an up and down reciprocating motion between the optical axis 204 and an outer edge of the desired aspheric surface 218a. In embodiments a stop 230 may be provided to inhibit the rocking bar from moving across the optical axis (although other means for preventing the tool moving beyond the centre of the lens may also be employed). Stop 230 is schematically illustrated in Figure 2 and may be implemented in a variety of ways. For example in an alternative approach rocking bar 202 may be provided with a projection illustrated by dashed lines 230a to abut the template 216 when the rocking bar is aligned with the optic axis. The rocking bar may be driven relatively slowly, for example making one pass of the lens surface every few seconds or minutes. Preferably, however, the tool is not moved across the surface of the lens or mirror so slowly that changes in temperature and consequent changes in the lengths of the flexible strips and/or rocking bars gives rise to deviation of the aspheric surface from that desired. In one embodiment the rocking bars carry a diamond tool as described further below from the axis of the lens to its edge in around a minute, making cuts of depth of order 25microns (0.001 inch).

As the rocking bar moves up and down the point of contact of the rocking bar with the template surface 216a moves between points 232a (on the optical axis) and 232b. These points define the limits of the centre of curvature at the centre and edge of aspheric surface 218a respectively. Thus, for example, the distance between the tip of the tool 210 and the 'apex' of the cam surface, that is the limit of contact 232a on the optical axis, defines the axial radius of curvature of surface 218a (the radius of curvature along the optical axis), which in turn determines the focal length of surface 218a.

The tool 210, schematically illustrated in Figure 2, has its axis aligned with the fiducial surface 202a of the rocking bar that is aligned along a tangent to the cam surface. In embodiments tool 210 comprises a small, diamond-impregnated tool rotating at high speed. The skilled person will appreciate, however, that the tool may be selected according to inter alia the desired smoothness of the glass surface, the depth of cut, the pressure applied, the rate of radial movement of the tool, the rate of rotation of the lens on its spindle, the average size of the diamond fragments in the grinding tool and so forth. Similarly it will be appreciated that tool 210 may be either a grinding tool or a polishing tool.

Figure 3 shows details of a preferred tool and tool support for the grinding machine of Figure 2. The tool support is provided by cross-member 206 of yoke 208 and has an axis 300 positioned coincident with the optical axis of the lens or mirror when the point of contact of the rocking bar is at point 232a, and may be moved vertically above the optical axis of the lens (where 'vertical' is defined by the plane in which the rocking bars 202 move). The tool 210 comprises a shaft 302 driven by a motor 304 and bearing a diamond-impregnated lap 306 of small or very small diameter. A formation in cross- member 206 provides a stop 308 for the tool 210 and a spring 310 urges the tool against this stop and towards the surface 218a to be cut or polished. This allows the tool 210 to pass over high spots grit and the like, and the end stop 308 prevents the tool moving any further than a set distance towards the surface 218a being cut, thus precisely defining the desired surface. The pressure of spring 310 also helps to reduce end-play.

Typically the diamond-impregnated tool rotates at a few thousand rpm and is provided with generous water cooling/lubrication. For fine grinding the diamond-impregnated lap may be replaced by a small cast iron tool rotated on the same axis. As previously described, the tool is mounted with its axis of rotation in the plane of the lower face of the straight portion of the flat springs 212, and intersecting the optical axis 204 of the lens/mirror. In embodiments the tool may have two semicircular active areas (as indicated in the figure). When grinding a convex surface such as a convex lens the face 306 of the tool may be flat or slightly concave, in the latter case having a radius or curvature greater than the distance from the convex (lens) surface to the further end of the cam/template surface 216a. Where a concave lens or mirror surface is being ground or polished, the face 306 of the tool may be convex, with a radius or curvature shorter than the distance between the lens/mirror and the near end of the cam/template surface 216a (as previously mentioned the nearer/further ends of this surface are illustrated by points 232a, b). as the skilled person will appreciate, In some preferred embodiments the tool is fed with a watery paste of fine carborundum or emery powder. Referring next to Figure 4, this shows, schematically, an example of a carriage 400 for the optical element whose surface is to be ground. (This is omitted in Figure 2, for clarity). The carriage comprises a base 402 supporting a smoothly running spindle 404 coincident with the optical axis 204 of the element to be ground, to which a flat, cast iron tool 406 can be screwed. The lens 218 or mirror is stuck to the tool with pitch. The spindle is driven by a motor 408, or a belt and pulley mechanism, at typically between 10-100rpm, for example around 50rpm. The carriage is moveable to allow the lens or other optical element to be advanced towards the grinding tool 210. In embodiments movement of the carriage is controlled by a micrometer screw arrangement 412, in embodiments the carriage being urged towards the grinding tool by a spring 414 (or other mechanism such as a weight, cord and pulley) and the movement of the carriage is controlled by a stop 416 which bears against micrometer screw 412, for controlled forward motion of the carriage. The carriage 400 has a traverse, say of 25mm, limited by the micrometer screw arrangement 412. Flexibility of the positioning of the cam is given as the apparatus is designed such that the cam can be moved along the base 402 and secured in different locations separated by increments of, in this example, 12.5mm along the direction of the optical axis 204. Alternatively, and potentially preferably, the micrometer screw and spring 414 may be arranged so that the force applied by the spring (or springs) 414 acts substantially in line with, and at the same point as, the restraining thrust applied by the micrometer screw 412.

The arrangement shown in Figure 2 illustrates grinding of a convex surface, but the tool 210 on the yoke 208 may be reversed, as indicated in Figure 5, for grinding of a concave surface, such as the concave surface 500a of a mirror 500. When configured for grinding a concave surface the cross-member 206 of the yoke may be extended in a central region around the optical axis to facilitate access of the tool to the central, deeper portion of the concave surface.

Optionally (though not shown in the figures) a tensioning arrangement may also be employed to hold the fiducial surface of a rocking bar 202 against the template surface or cam (rather than relying upon gravity. In embodiments this may be achieved using a pair of coil springs in tension, with the lower end of each spring attached to a fixing, for example a bolt, in the template near to a base plate of the machine, and the upper end of each spring attached to a fixing, for example a bolt, in the rocking bar, preferably near to the mid point of the region of the bar which makes contact with the cam. In one approach the lower end of each spring is located substantially directly beneath the midpoint of the region of the template surface/cam in contact with the rocking bar (so that the force is substantially parallel to the direction of gravity). In an alternative approach the lower end of each spring is located substantially directly beneath the contact point 232a (so that the force is more nearly perpendicular to the surface of the evolute cam).

In embodiments of the top surface of the curved template (point 232a) is preferably level with the optic axis 204. The templates preferably sit upright, and preferably the template is provided with a vertical surface or edge at point 232a to facilitate setting the template at the right distance along the optical axis for the desired focal length. Preferably the rocking bar 202/tool 210 traverses substantially a complete single radius of the optical surface.

An example program listing for calculating the shape of the template surface ("guiding cam") in arrays X and Y, given a power series defining an aspheric optical surface (array D), is given below:

2013/050408

13

C Program Profil5.f to evaluate asphericities given a power series C defining a mirror and an assumed radius and centre of curvature.

C The program reads the number of steps, and greatest distances

C off axis at which the surface height is to be computed, then

C the power series. Copied from Profil3.f and much edited.

C

implicit Real*l6 (Α-Η,Ο-Ζ)

real*4 X, Y, P, Q, R, S, xmin, ymin, xmax, ymax

Dimension D(20), X(520), Y(520), P(510), Q(510),

1 R(510), S(510), V(8), W(8)

character infile^*80, outfile*80, message*50, another*80

200 write (6,*) ' Name the input file...dat'

read(5, '(a) ') infile

open(7,file=infile,status='old',err=200)

210 write(6, *) ' and the output file... out'

read(5,'(a)') outfile

open(8,file=outfile,status='new',err=210)

220 write (6,*) 'and another output . . out'

read(5,'(a)') another

open( 10,file=another, status- new' ,err=220)

Write (8,10)

10 Format(1 H )

Write (8,18) infile, outfile

Write (10,10)

Write (10,18) infile, another

18 Format(1H ,'Using program profil5.f I/O = \2A15)

C Read the number of steps, the interval at which the profile is to

C be calculated, the radius of curvature of the nearest sphere, and

C Kdr to control drawing: 0 = no drawing, 1 = convex, -1 = concave.

1 Read (7,2) N, St, C, Kdr

2 Format(1 H ,I5,2F12.6,I5)

If(N.EQ.O) Go To 90

C Read the power series which defines the aspheric lens surface.

Read (7, 3) (D(l), I = 1 ,5)

3 Format(3E20.13)

Write (8, 10)

Write (8,4) C

4 Format(1 H .'Coefficients of power series. Mirror radius =',

1 F24.17)

Write (8,5) (D(l), I = 1 ,5)

5 Format(1 H .3E25. 6)

Write (8, 10)

Write (8,6)

6 Format(1H, ' Height Sphere Power Series',

V Difference Gradient')

Write (8,10)

Write (10,10)

Write (10,9)

9 Format(1H ,' Height Axial Radial')

Write (10,10)

C Find differential power series.

D(6) = 2.0D0^*D(1) D(7) = 4.0D0*D(2)

D(8) = 6.0D0^*D(3)

D(9) = 8.0D0*D(4)

D(10) = 10.0D0^*D(5)

Read (7, 20) (D(l), I = 11 , 14)

20 Format(4F15.6)

Call pgbegin (0, "?\ 1 , 1 )

xmin = Sngl(D(11))

xmax = Sngl(D(12))

ymin = Sngl(D(13))

ymax = Sngl (D(14))

C D(1 1) - D(14) are corners of box.

Call pgenv (xmin, xmax, ymin, ymax, 1 , 0)

Write (message, 230)

230 Format(1 H , 'Cross section of aspheric lens') Call pglabel ('Axial mm', 'Radial mm' , message) Call pgsfs (2)

Call pgsls (1)

Call pgiden

C Draw optical axis.

X(1) = xmin

X(2) = xmax

Y(1 ) = Sngl(O.O)

Y(2) = Y(1)

Call pgsls (3)

Call pgline (2,x,y)

Call pgsls (1)

C Outer loop increments the distance off axis by St, N times.

H = 0.0Q0

L = 5

V(1) = 0.0

V(2) = 100.0

W(1) = 0.0

W(2) = 0.0

Do 50 K = 1 ,N

H = H + St

L = L +1

C First calculate the depth of the sphere at radius H

Sags = C - Qsqrt(C*C - H*H)

C Inner loop evaluates the power series, and its gradient.

Sagp = D(5)*H*H

Grad= D(10)*H*H

Do 70 J = 1 ,4

Sagp = (Sagp + D(5-J))*H*H

Grad= (Grad+ D(10-J))*H*H

70 Continue

Grad = Grad/H

Diff = Sagp - Sags

Write (8,7) H, Sags, Sagp, Diff, Grad 7 Format(1 H ,F8.2,4E16.8)

V(3) = Sagp T B2013/050408

15

W(3) = H

V(4) = V(3) + 100.0

W(4) = W(3) - 100.0*Grad

Call POINTX (V,W)

C Guiding cam in arrays X and Y.

X(K) = Sngl(V(5))

Y(K) = Sngl(W(5))

C Power series surface in arrays P and Q; sphere in arrays R and S.

P(K + 1) = Sngl(Sagp)

Q(K + 1 ) = Sngl(H)

R(K + 1 ) = Sngl(Sags)

S(K + 1) = Sngl(H)

If (N.EQ.50) Write (10,8) H, V(5), W(5)

8 Format(1H , F9.3.2F15 8)

V(1) = V(3)

W(1) = W(3)

V(2) = V(4)

W(2) = W(4)

If (N.EQ.500.and.LGE10) Then

Write (10,8) H, V(5), W(5)

L = 0

Endif

50 Continue

P(1) = 0.0

Q(1) = 0.0

R(1) = 0.0

S(1) = 0.0

Call pgline (N,x,y)

Call pgpt1(X(1), Y(1), 9)

Call pgpt1(X(50), Y(50), 9)

Call pgline (N+1 ,p,q)

Call pgsls(2)

Call pgline (N+1 ,r,s)

If (Kdr.EQ.0) Go To 89

C Kdr = 0 cancels the remainder of the drawing.

C Draw tangent beam. N.B. This code for lenses or convex mirrors.

C Thickness of flexible, flat spring, and of the tangent beam.

Tfs = 0.5

Tb = 4.0

X(1) = X(35)

Y(1) = Y(35)

X(2) = P(35)

Y(2) = Q(35)

DX = X(1) - X(2)

DY = Y(2) - Y(1)

DL = Sqrt(DX*DX + DY^*DY)

X(1) Sngl(X(1) + Tfs*DY/DL)

Y(1) = Sngl(Y(1) + Tfs^*DX/DL)

X(2) = Sngl(X(2) + Tfs^*DY/DL)

Y(2) = Sngl(Y(2) + Tfs^*DX/DL)

C Kdr = 1 for a convex surface, otherwise concave.

If (Kdr.EQ.1) Then

X(3)= Sngl(1.1^*X(2) - 0.1^*X(1)) Y(3) = Sngl(1.1^*Y(2) - 0.1^*Υ(1 )) X(4) = Sng)(1.2*X(2) - 0.2*X(1)) Y(4)= Sngl(1.2*Y(2) - 0.2*Y(1)) Else

X(3) = Sngl(0.8*X(2) + D.2*X(1 )) Y(3) = Sngl(0.8^*Y(2) + 0.2*Y(1)) X(4)= Sngl(0.9*X(2) + O.I*X(1)) Y(4) = Sngl(0.9^*Y(2) + 0.1*Y(1 )) C Save X(2), Y(2)

X(12) = X(2)

Y(12) = Y(2)

X(2) = X(3)

Y(2) = Y(3)

Endif

X(5) = Sngl(X(4) + Tb*DY/DL)

Y(5) = Sngl(Y(4) + Tb*DXflDL)

X(6) = Sngl(X(3) + Tb*DY/DL)

Y(6) = Sngl(Y(3) + Tb^*DX DL)

X(7) = Sngl(X(2) + Tb*DY/DL)

Y(7) = Sngl(Y(2) + Tb*DX/DL)

X(8) = Sngl(X(1) + Tb^*DY/DL)

Y(8) = Sngl(Y(1) + Tb*DX/DL)

V(1) = X(50) + 3.0Tb

W(1) = Y(50) + 10.0

V(2) - V(1)

W(2) = Y(50) - 10.0

V(3) = X(1 )

W(3) = Y(1 )

V(4) = X(2)

W(4) = Y(2)

Call Pointx (V, W)

X(10) = Sngl(V(5))

Y(10) = Sngl(W(5))

X(9) = Sngl(X(10) + Tb*DY/DL)

Y(9) = Sngl(Y(10) + Tb*DX/DL)

X(ll) = X(D

Y(11) = Y(1)

Call pgslw(2)

Call pgsls(2)

Call pgline(11 ,x,y)

C Draw an arrow indicating cutting tool.

If (Kdr.EQ. I)Then

X(2)= Sngl(X(2) - 0.05^*(X(2) - X(4))) Y(2)= Sngl(Y(2) - 0.05*(Y(2) - Y(4)))

Else

X(2)= Sngl(X( 2) - 0.10^*(X(12) - X(4))) Y(2) =Sngl(Y(12) - 0.10*(Y(12) - Y(4))) Endif

X(1)= X(4)

Y(1)= Y(4)

Call pgsls(1)

Call pgarro(X(l), Y(1), X(2), Y(2))

C Draw solid cross-piece of flat bar. 16a

X(1) = X(5)

Y(1)= Y(5)

X(2) =X(6)

Y(2) =Y(6)

Call pgline(5,x,y)

C Draw flat flexible spring .

X(1)= Sngl(X(11) - Tfs*DY/DL)

Y(1)= Sngl(Y(11)- Tfs*DX/DL)

X(2) = Sngl(X(1) - 42.0^*DX/DL)

Y(2)= Sngl(Y(1) + 42.0*DY/DL)

X(3) = Sngl(X(2) +Tfs*DY/DL)

Y(3) = Sngl(Y(2) + Tfs*DX/DL)

Do 30 I = 4,19

X(l) = Sngl(X(l+31 ) + Tfs*DY/DL)

Y(l) = Sngl(Y(l+31) +Tfs*DX/DL)

30 Continue

X(20)= Sngl(10.0^*X(19) - 9.0*X(18))

Y(20) =Sngl(10.0*Y(19) - 9.0*Y(I8))

X(21)= Sngl(10.0^*X(50) - 9.0*X(49))

Y(21)= Sngl(10.0*Y(50) - 9.0*Y(49))

X(22) =X(50)

Y(22) =Y(50)

Call pgslw(1)

Call pgline(22,x,y)

89 Call pgend

90 Stop

End

C

Subroutine POINTX (X.Y)

Implicit Real^* 6(A-H,0-Z)

Dimension X(5), Y(5)

C Given two straight lines defined by (X(1), Y(1)), (X(2), Y(2)) C and (X(3), Y(3)), (X(4), Y(4)) find their intersection, and C return to the main program with the result in (X(5). Y(5)).

A = Y(2) - Y(l)

B = X(1) - X(2)

C= Y(1)*(X(2)-X(1)) + X(1)*(Y(1)-Y(2))

D= Y(4) - Y(3)

E = X(3) - X(4)

F= Y(3)^>(X(4)-X(3)) + X(3)^*(Y(3)-Y(4))

X(5) = (B*F- E*C)/(A*E - D*B)

Y(5) = (C*D- F*A)/(A*E- D^*B)

C Write (8,1) X(5), Y(5)

C Write (6,1) X(5), Y(5)

1 Format(1H .3FI5.4)

RETURN

END 17

A variant of the tensioning arrangement of Figures 2b and 2c is shown in Figures 6a and 6b, where the tensioning arms are mounted on the pivot points 222 which themselves are mounted on the cam 216. This arrangement may be preferable as it avoids application of any significant force to the cam 216 or its mounting. The apparatus may be designed such that it has a fiducial surface 601 at one of the limits of contact on the cam; then the perpendicular distance from fiducial surface 601 to the tool 210 is equal to the axial radius of curvature of the optical element (lens or mirror). Embodiments of the machine may be employed to grind a wide range of aspheric surfaces including, but not limited to: concave paraboloidal mirrors of a range of apertures; lenses corrected for spherical aberration; the convex mirror of a 3 mirror telescope (in which the asphericity varies with the sixth power of the distance off-axis and with the opposite sign of a hyperboloid); and other parabolic and hyperbolic surfaces, including mirrors with a very short focal ratio (less than unity, for example f/0.25); and other aspheric optical surfaces. Embodiments of the machine may be employed to grind aspheric optical surfaces using a grinding wheel, or for Single Point Diamond Turning (SPDT) of aspheric optical surfaces. For the case of SPDT, there is no need for a motor in order to drive the grinding wheel. However, for SPDT, the lens spindle should be driven much faster than for use with a grinding wheel. However embodiments of the machine are less preferably used to fabricate surfaces with a very long radius of curvature, and the described embodiment is not able to produce a surface with both convex and concave parts (and hence a point of inflection), such as a Schmidt camera correcting plate.

The machine we have described is advantageous over multi-axis CNC machines as it has fewer axes, since the axis about which the working parts of the machine pivot is an axis that moves (both along the axis of the lens and perpendicular to that direction) as a result of the working parts of the machine rotating around the aspheric form of the lens. A further advantage of the machine is that it can be designed to exhibit an inherently very high level of stiffness. A high stiffness is of major importance in the design of machine tools used for grinding lenses. Moreover, the machine is advantageous as it can be operated without exploiting laser interferometers to control the position of the tool 210. 18

No doubt many other effective alternatives to those described will occur to the skilled person. It will be understood that the invention is not limited to the described embodiments and encompasses modifications apparent to those skilled in the art lying within the spirit and scope of the claims appended hereto.

Claims

19 CLAIMS:

1. An aspheric optical surface grinding machine, the machine comprising:

a frame, said frame defining an optical axis of an optical element to be provided with an aspheric optical surface;

a template mounted on said frame and having a curved template surface representing a desired aspheric surface of said optical element;

at least one rocking bar mounted on said frame and able to rock in a first plane, wherein said rocking bar has a fiducial surface arranged to bear against said template surface, such that as said rocking bar rocks said fiducial surface remains in contact with and rolls over said template surface and a point of contact of said fiducial surface with said template surface moves along said template surface, wherein said fiducial surface defines substantially a tangent to said template surface at said moving point of contact and is linear and rigid in a direction of said tangent;

a tool support, attached to said rocking bar, to support a tool for shaping said optical surface, wherein said tool support has an axis located in a plane parallel to said first plane and containing said optical axis and is directed substantially parallel to said tangent; and

a system to hold said rocking bar to inhibit said rocking bar from slipping longitudinally along a direction of said tangent.

2. A grinding machine as claimed in claim 1 wherein said system to hold said rocking bar comprises a flexible strap attached between said rocking bar and said curved template or frame, and means for tensioning said strap.

3. A grinding machine as claimed in claim 2 wherein said means for tensioning said strap comprises an elastic element mounted such that tension in said elastic element remains aligned substantially parallel to said tangent and as said rocking bar rocks.

4. A grinding machine as claimed in claim 2 or 3 wherein said means for tensioning said strap comprises an arm having a pivot longitudinally located, in a longitudinal direction defined by said optical axis, between limits of contact of said fiducial surface with said template surface, and a tensioned elastic element coupling said arm to said rocking bar. 20

5. A grinding machine as claimed in any preceding claim wherein said tool support comprises a tool stop to limit travel of said tool in said direction substantially parallel to said tangent, and bias means to urge said tool towards said stop.

6. A grinding machine as claimed in any preceding claim further comprising a rocking bar stop to inhibit motion of said rocking bar beyond a second plane

perpendicular to said first plane and containing said optical axis.

7. A grinding machine as claimed in any preceding claim comprising a pair of said rocking bars, one to either side of said optical axis, defining a yoke, and a

corresponding pair of said templates, one to either side of said optical axis; and wherein said tool support is provided in a cross-member of said yoke.

8. A grinding machine as claimed in any preceding claim further comprising said tool, in particular wherein said tool comprises a rotating tool having an axis of rotation aligned substantially parallel to said tangent.

9. A grinding machine as claimed in any preceding claim further comprising a reciprocating drive for said at least one rocking bar.

10. A grinding machine as claimed in any preceding claim further comprising a linear feed for said optical element, to feed said optical element along said optical axis towards said tool, wherein said linear feed comprises a moveable feed stop and bias means to bias said optical element towards said feed stop.

11. A grinding machine as claimed in any preceding claim wherein said optical surface is a convex optical surface, and wherein said tool support is configured to mount said tool such that a face of said tool is directed towards said template surface in said direction substantially parallel to said tangent.

12. A grinding machine as claimed in any preceding claim wherein said optical surface is a concave optical surface, and wherein said tool support is configured to mount said tool such that a face of said tool is directed away from said template surface in said direction substantially parallel to said tangent. 21

13. A grinding machine as claimed in any preceding claim wherein said template surface defines an evolute of said aspheric surface.

14. A grinding machine is claimed in any preceding claim wherein said template is user detachable.