The method described in chapter 8 for grinding and polishing the diagonal is not the one usually pursued in the making of an optical flat, although it is capable of a high order of accuracy. Of course, any means of grinding that will result in an apparently perfectly flat surface, when tested against a high-quality straight-edge, should be sufficiently reliable to warrant polishing, in the expectation of producing a perfect plane. A master flat of known precision is essential, however, if the operation on a single surface is to be successfully concluded.
When a master flat is lacking, it is customary to proceed by the three-disk method for the operations of grinding, polishing, and testing. Three glass disks of equal diameter, and each not less than one eighth this diameter in thickness, are marked for identification, and are then ground together in a logical sequence, so that each of them will be accorded an equal amount of work against each of the others in every possible combination, the endeavor being to produce an infinite radius on each of the surfaces. The sequence of the grinding is as follows: a on b, b on a, a on c, c on a, b on c, c on b, a on c, c on a, a on b, b on a, c on b, and b on c. The identifying letters can be painted in one or more places on the sides of the disks.
One charge of abrasive is thoroughly ground down in each position, and the whole sequence should be gone through with each grade; thus each surface has the benefit of eight charges. Quarter-diameter strokes should be used throughout. As when fine grinding the mirror, occasionally separate the disks and redistribute the abrasive with the fingers. The heavy pressure that is normally maintained in grinding should be relaxed for the last half of the sequence when using No. 600, and little if any pressure should be used on the final grade. Ample grinding with each grade of abrasive is afforded each surface, so do not spend time looking for pits or testing with a straightedge. Properly worked, each of the surfaces should emerge flat to a wave length of light or less, as disclosed by the interference test when the disks have been sufficiently polished to yield a reflection. (See Chapter 8 for a discussion of the light source and interference test.)
The surfaces of plate-glass disks are manufactured reasonably plane, so if they are to be used for the flats, grinding can begin with No. 600. If pyrex, by far the best material (except for fused quartz), is used, the grinding must commence with No. 80 carbo. The back surfaces of pyrex mirror blanks are surrounded with a wide roughened border that makes difficult the viewing of the interference bands out near the edge, so it is customary first to grind and polish those surfaces to a reasonable plane, the rough grinding being best done on a large slab of scrap plate glass.
It is desirable to use two laps in polishing, one being pressed while the other is working, with the best flat used for pressing. Plate-glass tools of suitable thickness can be used for the lap foundation, and the pitch must be on the hard side; in fact, it is difficult to have the lap too hard for flat making. The molded lap with evenly spaced facets (see Chapters 5 and 8) is admirably suited for this work, as it is markedly superior to the channeled lap in freedom from zones. For the polishing, one-quarter to one-third diameter strokes should be used. Polishing periods may be 15 or 20 minutes long, followed by at least half an hour of cold-pressing. About 30 pounds of weight should be used in pressing, equally distributed at three points on the top of the flat, and since neither the bottom of the tool nor the top of the bench will be perfectly flat, a thin cushioning material, such as sheet rubber 1/16" thick, should be placed between them. Cerium oxide or Barnesite, used as the polishing agent, will materially speed up the work.
Convexity is corrected in the normal way, with the flat on top, and by extending the stroke length to as much as half-diameter. A small amount of concavity, of the order of a wave length or so, can be corrected in the same way, but using short strokes; for greater error it may be necessary to invert and polish with the flat face up. There will be little danger of turning the edge by this procedure, provided the lap is sufficiently hard and the strokes are kept short. Frequently, a surface consisting of a compound curve will crop up; in other words, a real cross section like that shown in Fig. 32c will be present, the center of the flat being convex, and the edge zones concave. Except in a very mild form, such a condition is rare with a hard lap. It is corrected by polishing with the lap on top, using one-third strokes, the effect being to throw the whole surface convex, after which the flat is placed on top, and the convexity reduced with as long a stroke as can be handled without introducing concavity at the center. After testing, and before resuming polishing, you must first establish contact by means of hot-pressing, allowing the flat to stand on the lap for at least one hour, under 30-pound pressure.
On account of temperature effects, far more pronounced than in the case of the concave mirror, figuring will have to proceed slowly. For a quarter-wave tolerance, the relatively liberal conditions prescribed for mirror making are satisfactory, but as the figure approaches to within 1/10 of a wave of flatness, as much as three hours may have to elapse, following an interval of polishing, before an accurate test can be made. During this period, the room must be free from drafts, and the temperature should not vary by more than one degree. Do not handle the flats any more than is necessary to place them in contact for testing and to space the bands properly.
For best accuracy, space the bands about 1" apart, and use only a diametric band for testing. With a straightedge (see Fig. 55) and dividers, curvature amounting to 1/10 of the band separation, or 1/20 of a wave length of the light used, is easily measured. An appearance like that in Fig. 52, left, found on all three combinations, will indicate absolute flatness of all three disks. Zonal errors, disclosed by wiggles in the bands, are either depressions or ridges, the direction of the wiggle indicating which is the case. If caused by a ridge or hill, the curvature of the bands is convex toward the wedge opening between the disks; if caused by a depression or hollow, the bands are concave toward the wedge opening. The precision of surface necessary depends on the purpose for which the flat is to be used. For the testing of diagonals, prism faces, filters, and sextant mirrors, flatness to a quarter wave (for a 6-inch disk) is acceptable. For a coelostat, or for the testing at the focus of achromatic objectives, paraboloidal mirrors, or Cassegrainian systems, the departure from flatness should not exceed 1/10 of a wave. One of the surfaces, or all three, should be figured to within these limits.