Surface Form Tolerances

Target Surface vs. Machined Surface

Surface Form Parameters

Only sectional views of the 3D optical surface are shown above.

Syntax according to ISO 10110

3/ A(B/C) RMS_t < D_t; RMS_i < D_i; RMSa < D_a; λ = E

• A = Sagitta error ≙ PV of best-fit sphere; [nm] or [fringes]
• B = PV of irregularity; [nm] or [fringes]
• C = PV of rotationally invariant irregularity; [nm] or [fringes]
• D_t = RMS of sagitta error; [nm] or [fringes]
• D_i = RMS of irregularity; [nm] or [fringes]
• D_a = RMS of rotationally variant irregularity; [nm] or [fringes]
• E = Reference wavelength for fringe spacing; [nm]

Example	Meaning
3/ – (1); RMS a < 0.1; λ = 546 nm	B = 1 fringe = 1 × λ/2 = 0.5 × 546 nm = 273 nm; Da < 0.1 fringe
3/ 2(1/0.5); λ = 632.8 nm	A = 2 fringes; B = 1 fringe; C = 0.5 fringe; 1 fringe = 0.5 × 632.8 nm = 316.4 nm
3/ –; RMSt < 100 nm; RMSi < 30 nm; λ = 546 nm	Dt < 100 nm; Di < 30 nm

Fringes	λ	λ = 546 nm
1 fringe	λ/2	273 nm
0.5 fringe	λ/4	136.5 nm
0.2 fringe	λ/10	54.6 nm
0.1 fringe	λ/20	27.3 nm
0.04 fringe	λ/50	10.92 nm

Basic Rules

If tolerances are specified without a unit they are given in fringes. According to ISO 10110-5:2016-04 the reference wavelength always has to be specified. Please note that in older versions of the standard λ = 546 nm (Hg e-line) is assumed if no reference wavelength is specified.

How Flat is Flat?