Each fringe typically represents ½ wavelength of optical path difference, allowing surface error to be quantified by fringe count.

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Flatness alone does not fully describe a surface. Optical specifications often break surface accuracy into two components: power and irregularity.

Power refers to the large-scale spherical curvature of a surface—essentially how much the surface bows away from flat.

It is measured by comparing the test surface to a reference surface (flat or spherical for lenses) . The resulting interference pattern often forms concentric rings, known as Newton’s Rings.

• More rings = greater spherical deviation from the reference
• The number of fringes (after automatic tilt removal) corresponds to the magnitude of error
• Each fringe represents ½ wavelength, so:
  surface deviation = fringe count × ½λ

Power is considered a low-order error, which can often be compensated for within the user’s application.

Irregularity describes the small-scale, localised deviations from the ideal shape once power has been removed.

In practical terms:

• Power indicates whether the surface is “bowed”
• Irregularity indicates how randomly distorted the surface is

Irregularity is assessed by observing how much the fringes deviate from either a perfectly spherical or flat ideal shape

Total surface deviation is a combined measure of all surface errors—both low-order (power) and high-order (more random)  (irregularity).

It is typically derived from:

• Interferometric surface maps
• Profilometry measurements

This value represents the overall deviation across the full aperture of the optic and provides a useful single-number indicator of surface form error.

Key concept:
Total surface deviation includes all measurable errors and provides a basic overview of surface accuracy.

Flatness is typically defined using recognised standards such as ISO 10110.

Key points:

• ISO flatness specifications are often referenced at 546 nm
• Specifications may be expressed in terms of power and irregularity

Example ISO notation:

• 3/5(1) → 5 fringes of power and 1 fringe of irregularity (within a specified aperture)

Typical conventions include:

• Units: fringes (waves) or fractions of a wavelength (λ)
• Clear aperture (CA): often specified as a percentage (e.g. 85% CA)
• Clear aperture may be defined as circular or elliptical on square components
• Infrared components are often specified at 10.6 µm, which can make equivalent flatness tolerances appear less stringent numerically

Example specification:

Flatness: 3 fringes over 85% CA @ 632.8 nm

For transmissive optics, flatness is often extended to Transmitted Wavefront Error (TWFE).

TWFE measures how much the optical wavefront is distorted as it passes through the component, incorporating:

• Surface flatness (both faces)
• Material refractive index
• Material and stress-induced homogeneity

Unlike surface flatness alone, TWFE reflects the optical performance of the entire component, not just its surface geometries.

Reflected error measures the deviation of a perfectly flat wavefront upon reflection from the optic’s surface.

It is determined again using  an interferometer, with the analysed result being exactly double the part’s surface error (regardless of refractive index)

Reflected flatness is particularly important for:

• Mirrors
• Beam splitters

It indicates how accurately a surface can reflect light without introducing aberrations.

Many applications, especially non-imaging applications, are able to function perfectly well with optics specified relatively loosely (for example 2 fringes per inch). However, these can add together within a multi-optic system so care should still be taken.

More demanding applications, such as high-resolution imaging or laser optics, sometimes require what’s known as ‘diffraction limited performance’. Generally, such a condition requires a total transmitted wavefront error (of all optical surfaces combined) to be better than  λ/4 (peak to valley), or more precisely the RMS error to be better than λ/14 (the rayleigh criterion).

Given the high refractive index of certain IR materials (Ge, Si, ZnSe), the resultant transmitted wavefront error through an optical component can be significantly higher than total (combined) surface error. However, if diffraction limited performance is a requirement, this is often more than mitigated by the longer design wavelength (eg 10.6 um in the case of a CO2 laser) making λ/14 (RMS) easier to achieve.

A significant trade-off therefore comes into play between price and performance when looking at surface flatness so a clear understanding of the application’s needs can be very important.

When producing optics with a flatness specification, several factors must be considered:

• Thickness – thinner components are more difficult to polish to high flatness
• Clear aperture – edge roll-off reduces flatness near the perimeter, hence the need to define a usable aperture
• Material – some materials are inherently more difficult to polish to high flatness
• Other specifications – requirements such as surface finish, parallelism, or coatings can influence achievable flatness
• The required surface quality (scratch-dig) and surface finish (roughness, Rq)