The surface figure, or surface quality or surface cosmetics all refer to the deviation between an actual optic and its ideal surface. There are basically two set of information that are commonly given by manufacturers: the surface flatness and what is referred to as “scratch-dig”.

Why is it important?

Well, an optic with a bad rating on surface flatness will introduce some wavefront distortions, which are responsible for aberrations and bad quality focus. Aberrated wavefront leads to poor Strehl ratio (ratio of the observed peak intensity at the image plane compared to the theoretical maximum peak intensity of a perfect optical system), so poor optics makes one loose valuable optical power at focus. Plus scratches or digs on an optic create diffraction and stray light, which no one wants either.

Surface flatness

This is the measurement of the difference between the actual surface of the optic and the surface it would have if it was defect-free. There are two main way to measure it, the most common is called “peak-to-valley” (P-V). This is the difference between the “highest” and “lowest” parts on the surface of the optic, those “top” and “bottom” being defined as the local difference between the actual optic and the ideal one. Of course this ignores the curvature of the optics, which is not a defect. We consider this method of measuring defects on optic as inaccurate and misleading: it is a maximum measurement, and it does not say how many peaks and valley there are on the whole surface. Consequently it is difficult to predict how an optic will perform with this sort of measurement. An optical system having a large P-V error may actually perform better than a system having a small P-V error. Unfortunately it is by far the most widespread flatness quality control in the industry.

A much better measurement is the RMS (Root Mean Square) value of the flatness. This technique involves measuring a substantial amount of the optic’s surface at many points and then calculating the standard deviation of the surface from the ideal form. This measurement has direct mathematical implications: for instance it is possible to calculate the Strehl ratio from it.

Once again, in short the Strehl ratio is a very good indication on how much power you get at the image plane of the optical system versus what power you will get from an ideal aberration-free system. Once the Strehl ratio has been calculated, the quality of the optical system may be ascertained using the Maréchal criterion. The Maréchal criterion states that a system is regarded as well corrected if the Strehl ratio is greater than or equal to 0.8, which corresponds to an rms wavefront error λ/14. For instance an optical system introducing a λ/3 RMS deformation will have his actual power at focus reduced to approximately 3% of its theoretical power. The reason for this drop in power at the focus is that some interferences are created in the focus, with different rays arriving with a different phase.

Since most manufacturers are specifying their optics flatness in peak-to-valley, here is a short comparison of what one should expect. This is without guarantee: as explained above, peak-to-valley is imprecise and misleading.

Scratch-dig

This is yet another very subjective quality measurement. Scratch-dig, sometimes called surface quality relates to the number and apparent size of visible defects, typically scratches and pits (called digs), on the part surface. While this may seem straightforward, probably no optical specification causes greater confusion. The problem arises because the assessment of scratches and digs is performed using a purely visual, non-quantitative comparison to a set of standards which conform to the US military specification MIL-O-13830. This situation arose because the specification was developed many years before the advent of the laser, when surface quality was primarily a cosmetic consideration without performance information. Scratch-dig is specified by two numbers, such as 40-20. The first number is the maximum width allowance for a scratch measured in microns, and the second is the maximum diameter for a dig in hundredths of a milimetre. So 40-20 would permit a scratch width of 0.04mm and a dig diameter of 0.2mm

This measurement is obviously badly limited: not only does it entirely rely on a visual inspection, but there is no measure of irregularities depth and scratches length, nor of their number, nor of their position (centre being worse). The problem is that this measurement has the potential to give important information on the optic. Small size defects are responsible light scattering, loss of contrast and stray light which can damage sensitive components in high power applications.

A much better measurement would be the Fourier transform of the surface of the optic, if this were available from manufacturers. Once again to help people getting an idea of what they are getting, here is a comparison of the average scratch-dig quality from quality manufacturers. Just keep in mind how imprecise this measurement is, though.

This is the material from which an optic is made. Although any material which is transparent at the working wavelength can be used as an optical substrate, materials such as plastic or common glass have poor reliability. Most commonly available substrate are BK7, Fused silica, Magnesium Fluoride (MgF₂) and Calcium Fluoride (CaF₂).

Typically, most imaging in the visible or near infra-red applications will be satisfied with BK7. This is an inexpensive material with excellent transmission between 400 nm and 2 µm. Its hardness provides a good trade-off between resistance to deformation and resistance to scratches.

For non-critical application which needs a heat resistant substrate, Pyrex^® offers a cheaper alternative, but this substrate is not suitable to create a good image, and is ruled out for any laser application.

Demanding laser applications will prefer fused silica. This material can be UV grade (called “UV fused silica” to differentiate) and be used with wavelengths as low as 180 nm and up to 2 µm. Its high homogeneity allows high damage threshold and better wavefront control. It also show no fluorescence or discolouration when exposed to radiation shorter than 290 nm. Its low thermal expansion coefficient would also lower the thermal lensing effects which are common in high power lasers.

Vacuum UV (typically less than 200 nm) will require Magnesium Fluoride (MgF₂). Its mechanical properties and UV transmission are ideal for this type of application. Since this is quite an expensive substrate, it is sometime replaced by Calcium Fluoride (CaF₂). Both material offers good transmission in the infrared up to 8 µm, however CaF₂ performs better in the infrared. MgF₂ has a slight birefringence, which demands careful alignment at manufacturing. MgF₂ is a rugged material which has good resistance to mechanical or thermal shock and is resistant to chemical etching: its hardness is nearly three times that of CaF₂, and its thermal expansion coefficient is nearly nine times lower. Both material have no water absorption line, which makes CaF₂ the material of choice for applications from 2 µm to 8 µm.

Very large optics, etalons and high accuracy interferometry mirrors (or any precision mirror requiring excellent flatness control) will generally be made using Zerodur^® (Schott). Rarely used in visible transmission because of its absorption in the blue region of the visible spectrum, it is a highly homogeneous, glass ceramic whose thermal and mechanical properties are extremely stable over a wide temperature range.

Polarisation control often require birefringent material. The two most common are calcite (CaCO₃) and crystal quartz (SiO₂). Calcite has a very strong birefringence and can be used from 400 nm up to 2.5 µm. It is the material of choice for polarizing prisms such as the Nicol prism, the Glan-Foucault prism, and the Wollaston prism. Calcite is a very soft material and extra care must be taken while manipulating it. Crystal quartz has a higher damage threshold but lower birefringence. It is often used in high damage threshold waveplates and Brewster windows. It is also good to notice that its transmission is still acceptable below 200 nm.

Difficult environments such as high temperature, high pressure, high thermal shock environments, or optics easily exposed to scratches and humidity might choose Sapphire. Its strength (extreme hardness) being its downfall, it is a really difficult material to polish, and high quality finish is not always possible. It transmits light from 150nm up to 6µm. It is also used with PbS, PbSe, and InSb detectors to match the spectral transmittance with the spectral sensitivity of the detector.

The three materials most commonly used in mid-far infrared are Zinc Selenide (ZnSe), Germanium (Ge) and Silicon (Si). Zinc Selenide is used when a high transmission is required since it is a very soft material. It transmits well up to 20µm. Germanium, used from 2µm to 20µm, has a much lower transmission but its hardness allow the optic to be thinner. It is not suitable for high laser power. Finally Silicon will be preferred for low-cost applications up to 7µm.

The next few articles will focus on helping you weight the importance of each characteristics of the optics you need for your application.

This is critical when building an optical system. For instance bad flatness will introduce wavefront deformation which will limit the quality of the image and surface irregularities will lower the damage threshold of the system.

When choosing an optic, one must consider the following specifications:

• optical substrate
• coating type and damage threshold
• usable wavelength range
• optic size and clear aperture
• hardness
• surface figure or flatness
• surface quality
• polarisation