Surface Flatness, also called Surface form deviation, is one of the most important specification of optical components. it is the standard deviation of an optical system from its ideal form. They are indicated on the drawing by 3/A(B/C). A is the maximum spherical sag error from test plate. A dash can be substituted for A where the radius tolerance is a dimension. B is the p-v maximum irregularity, and C is the maximum rotationally symmetric p-v figure error (best fit aspheric surface). The units are fringes (one half wavelength of 546.07 nm) and RMS specification for fringes can be used. For example, 3/4(1) implies the sag tolerance is 4 fringes and the p-v irregularity is no greater than 1 fringe. A callout of 3/-(2)implies a p-v irregularity of 2 fringes, and the radius of curvature is tolerance by the radius specification if the surface is spherical (untoleranced if plano).

**Fringe and irregularity**

When the test optic’s surface is placed against the reference surface, the shape of fringes that appear indicates the surface flatness of the tested piece. If both elements are evenly spaced straight and parallel, our optic is at least as flat as the reference optical flat. On the contrary, flatness errors appear when fringes are curved, the number of fringes between two imaginary lines, one tangent to the center of a fringe and one through the ends of that same fringe.

1 unit of fringe spacing corresponds 1/2 wavelength. Typically, 1λ flatness is considered commercial quality, λ/4 flatness is considered precision quality, and λ/20 is considered high precision quality.

**PV and RMS**

PV (Peak-to-Valley) is the measurement of the height difference between the highest point and the lowest point on the surface of the optical element.

RMS (Root-Mean-Square) describes the average deviation of the surface figure from the desired surface. It’s a more accurate measurement of surface flatness is RMS, as it considers the entire optic and calculates deviation from the ideal form.

An optical system with 20 nm as RMS of the irregularity is considered high precision quality, while another from 50 to 100 nm RMS is considered to be precision quality and higher numbers, such as 500 nm is commercial quality.