Optical flat

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.

If the surface is clean and reflective enough, rainbow colored bands of interference fringes will form when the test piece is illuminated with white light.

Most commonly, acetone is used as the cleaning agent, because it dissolves most oils and it evaporates completely, leaving no residue.

This process is usually performed dozens of times, ensuring that the surface is completely free of impurities.

A new tissue will need to be used each time, to prevent recontamination of the surfaces from previously removed dust and oils.

Testing is often done in a clean-room or another dust-free environment, keeping the dust from settling on the surfaces between cleaning and assembly.

Sometimes, the surfaces may be assembled by sliding them together, helping to scrape off any dust that might happen to land on the flat.

The testing is usually done in a temperature-controlled environment to prevent any distortions in the glass, and needs to be performed on a very stable work-surface.

Of all the lights, low pressure sodium is the only one that produces a single line, requiring no filter.

Sometimes, a diffuser may be used, such as the powder coating inside frosted bulbs, to provide a homogenous reflection off the glass.

The brightness of the reflected light depends on the difference in the path length of the two rays: If the gap between the surfaces is not constant, this interference results in a pattern of bright and dark lines or bands called "interference fringes" being observed on the surface.

These are similar to contour lines on maps, revealing the height differences of the bottom test surface.

The equation for the electric field of the sinusoidal light ray reflected from the top surface traveling along the z-axis is where

, so the brightness of the reflected light is an oscillating, sinusoidal function of the gap width d. The phase difference

Optical flats are extremely sensitive to temperature changes, which can cause temporary surface deviations resulting from uneven thermal expansion.

Merely handling the flats can transfer enough heat to offset the results, so glasses such as fused silica or borosilicate are used, which have very low coefficients of thermal expansion.

When measuring on the nanometre scale, the slightest bit of pressure can cause the glass to flex enough to distort the results.

By analyzing the patterns and their different phase shifts, the absolute contours of each surface can be extrapolated.

The interference fringes typically only form once the optical flat begins to wring to the testing surface.

The optical flat should usually never be allowed to fully wring to the surface, otherwise it can be scratched or even broken when separating them.

Sliding the flat in relation to the surface can speed up wringing, but trying to press the air out will have little effect.

When wringing first begins, there is a large angle in the air wedge and the fringes will resemble grid topography-lines.

If the surfaces are not completely flat, as wringing progresses the fringes will widen and continue to bend.

A single dark-fringe has the same gap thickness, following a line that runs the entire length of the fringe.

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.

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.

Another method involves exposing the flat to white light, allowing rainbow fringes to form, and then pressing in the center.

Therefore, hard glasses with low coefficients of thermal expansion, such as fused silica, are often used for the manufacturing material.

However, a few laboratory measurements of room temperature, fused-silica optical-flats have shown a motion consistent with a material viscosity on the order of 1017–1018 Pa·s.

This deformation has only been observed in fused silica, while soda-lime glass still shows a viscosity of 1041 Pa·s, which is many orders of magnitude higher.

Optical flats in case. About 2.5 centimetres (1 in) in diameter. The third flat from the left is standing on edge, showing the thickness.
A λ/20 optical flat that has been coated with aluminum, making a first-surface mirror
Two optical flats tested using 589 nm laser-light. At 2 inches (5.1 cm) in diameter and 0.5 inches (13 mm) thick, both surfaces are flat to within 1/10 of the wavelength of the light (58.9 nm), as indicated by the perfectly straight fringes.
Testing the flatness of surfaces with optical flats. The lefthand surface is flat; the righthand surface is astigmatic , with curvatures in two orthogonal directions.
An optical flat test in which the angular size of the light source is too small. The interference fringes only show up in the reflection, so the light needs to appear larger than the flat.
How interference works. The distance between the bright fringe (a) and the dark fringe (b) indicates a change in the light path length of 1/2 the wavelength, so a change of the width of the gap of 1/4 wavelength. So the distance between two bright or dark fringes indicates a change in the gap of 1/2 wavelength. The gap between the surfaces and the wavelength of the light waves are greatly exaggerated.
Two λ/10 flats at 589 nm. Although both surfaces have some irregularities, the test shows they are both flat relative to each other. As wringing progresses the thin fringes widen until only a single fringe remains.
A thermal image of an optical flat after handling for just a few seconds. The warmer areas increase the thickness of the flat over cooler areas, distorting the surface accordingly.
Optical flats being used to calibrate metal parts
  1. Initial wringing, 532 nm,
  2. Initial wringing, white light,
  3. Wringing, 1 hour,
  4. Wringing, 2 hours,
  5. Fully wrung,
  6. Fully wrung in white light. The window is slightly concave rather than convex.
A flatness test of a float-glass optical window . By placing a ruler across the image, adjacent to a fringe, and counting how many fringes cross it, the flatness of the surface can be measured along any line. The window has a flatness of 4–6λ (~2100–3100 nm) per inch.
An optical flat test in both green and red. The wavelengths are nearly harmonic opposites (green is λ/4 shorter), so the fringes overlap every fourth red-fringe (every fifth green-fringe), interfering to form yellow fringes.