page_title: Optical flat
section_title: Determining surface shape
hierarchical_section_title: Optical flat / Determining surface shape
caption_attribution_description: English: A precision glass window ground to a flatness of λ/10, resting upon an λ/10 optical flat, illuminated with both the green 532 nm light from a laser and white light from an incandescent bulb, showing interference fringes which reveal the unevenness of the surface. Image 1 shows that the fringes are fairly straight, with some small deviations, indicated that the surface of the window in very close to λ/10 flatness. The flat has slightly chamfered edges, which shows up as bends near the ends of the fringes. The bottom side of the flat is mirrored, which not ideal, masking some of the fringes. Image 2 shows the interference fringes in white light. Image 3 is after an hour of wringing, as the surfaces come closer to parallel. Image 3 is after 2 hours or wringing. Images 5 and 6 are taken after the surfaces have fully wrung, becoming parallel. Both the white-light test and the finger-pressure test show that the surface of the window is concave.
context_page_description: An optical flat is an optical-grade piece of glass lapped and polished to be extremely flat on one or both sides, usually within a few tens of nanometres. They are used with a monochromatic light to determine the flatness of other surfaces, whether optical, metallic, ceramic, or otherwise, by interference. When an optical flat is placed on another surface and illuminated, the light waves reflect off both the bottom surface of the flat and the surface it is resting on. This causes a phenomenon similar to thin-film interference. The reflected waves interfere, creating a pattern of interference fringes visible as light and dark bands. The spacing between the fringes is smaller where the gap is changing more rapidly, indicating a departure from flatness in one of the two surfaces. This is comparable to the contour lines one would find on a map. A flat surface is indicated by a pattern of straight, parallel fringes with equal spacing, while other patterns indicate uneven surfaces.
context_section_description: The fringes act very much like the lines on a topography map, where the fringes are always perpendicular to the wedge between the surfaces. When wringing first begins, there is a large angle in the air wedge and the fringes will resemble grid topography-lines. If the fringes are straight; then the surface is flat. If the surfaces are allowed to fully wring and become parallel, the straight fringes will widen until only a dark fringe remains, and they will disappear completely. If the surface is not flat, the grid lines will have some bends in them, indicating the topography of the surface. Straight fringes with bends in them may indicate a raised elevation or a depression. Straight fringes with a "V" shape in the middle indicate a ridge or valley running across the center, while straight fringes with curves near the ends indicate edges that are either rounded-off or have a raised lip.
  If the surfaces are not completely flat, as wringing progresses the fringes will widen and continue to bend. When fully wrung, they will resemble contour topography-lines, indicating the deviations on the surface. Rounded fringes indicate gentle sloping or slightly cylindrical surfaces, while tight corners in the fringes indicate sharp angles in the surface. Small, round circles may indicate bumps or depressions, while concentric circles indicate a conical shape. Unevenly spaced concentric circles indicate a convex or concave surface. Before the surfaces fully wring, these fringes will be distorted due to the added angle of the air wedge, changing into the contours as the air is slowly pushed out.
  A single dark-fringe has the same gap thickness, following a line that runs the entire length of the fringe. The adjacent bright-fringe will indicate a thickness which is either 1/2 of the wavelength narrower or 1/2 of the wavelength wider. The thinner and closer the fringes are; the steeper the slope is, while wider fringes, spaced further apart, show a shallower slope. Unfortunately, it is impossible to tell whether the fringes are indicating an uphill or downhill slope from just a single view of the fringes alone, because the adjacent fringes can be going either way. A ring of concentric circles can indicate that the surface is either concave or convex, which is an effect similar to the hollow-mask illusion.
  There are three ways to test the surface for shape, but the most common is the "finger-pressure test." In this test, slight pressure is applied to the flat, to see which way the fringes move. The fringes will move away from the narrow end of the wedge. If the testing surface is concave, when pressure is applied to the center of the rings, the flat will flex a little and the fringes will appear to move inward. However, if the surface is convex, the flat will be in point-contact with the surface in that spot, so it will have no room to flex. Thus, the fringes will remain stationary, merely growing a little wider. If pressure is applied to the edge of the flat something similar happens. If the surface is convex the flat will rock a little, causing the fringes to move toward the finger. However, if the surface is concave the flat will flex a little, and the fringes will move away from the finger toward the center. Although this is called a "finger" pressure test, a wooden stick or some other instrument is often used to avoid heating the glass (with the mere weight of a toothpick often being enough pressure).
  Another method involves exposing the flat to white light, allowing rainbow fringes to form, and then pressing in the center. If the surface is concave, there will be point-contact along the edge, and the outer fringe will turn dark. If the surface is convex, there will be point-contact in the center, and the central fringe will turn dark. Much like tempering colors of steel, the fringes will be slightly brownish at the narrower side of the fringe and blue on the wider side, so if the surface is concave the blue will be on the inside of the rings, but if convex the blue will be on the outside.
  The third method involves moving the eye in rela
caption: Initial wringing, 532 nm,Initial wringing, white light,Wringing, 1 hour,Wringing, 2 hours,Fully wrung,Fully wrung in white light. The window is slightly concave rather than convex.
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