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.

Nowadays, the vast majority of scientific and industrial optics have a thin-layer coating. With the increasing complexity of optical systems, non-coated optics can easily introduce ghost images, back reflections, and can in some instances be an safety hazard or destroy an expensive piece of equipment. On the other hand, thin-film coating introduce critical properties in the optics which use them. Here is an overview of the different most common coatings techniques available.

The simplest of all

The simplest coatings are made of thin layer of metal, such as aluminium, sliver or gold. They are used for broadband mirrors. The best reflectivity comes at higher price: aluminium (Al) is the cheapest (R=88%-92%), followed by silver (Ag, R=95%-99%) and then gold (Au, 98%-99%). But in the blue-violet part of the spectrum, only aluminium is suitable.

Dielectric coatings

These coatings use different thin layers of material (various metal oxides, calcium or magnesium fluorides) to create the desired effect. There are three major techniques used for dielectric coating: electron-beam deposition (E-beam), ion-assisted electron-beam (IAD) and ion beam sputtering (IBS). All of these process are quite similar in their principle. They consist in evaporating some coating material on the substrate. The difference lies in the deposition energy.

Because of the low energies involved when using electron-beam deposition, the thin film material contains bubbles and micropores, like a sponge. These will eventually fill with water, which will change the refractive index of the coating and thus the properties of the optics. (This is known as “environmental shifting”). The presence of water also lowers the damage threshold of the optics: when submitted to an intense light, the water will tend to vaporise and scrap off bits of the coating. Finally, even in the absence of water, the inhomogeneities of the coating layers lower the theoretical damage threshold. The positive points about this technology is that it is cheap, widespread and very versatile. The coating itself is also slightly flexible, which makes the optic more resistant to mechanical stress. Some of the major optics manufacturer only have access to that type of coating at the moment and outsource IBS-coated optics.

Ion-assisted electron-beam is an intermediate technique, between ion-beam sputtering and e-beam. So are its results.

Ion beam sputtering involves energies 100 times higher than e-beams. As a result the molecules of the coating layers form covalent bound when deposited. The result is free from bubbles or pores, more homogenous, more durable, have higher damage threshold and is more repeatable and controllable. They also show lower scattering and absorption properties, and overall higher specifications (more broadband, steeper transitions when needed, better spectral stability…). This is high precision coating, and the surface roughness can be controlled at better than 1 Å RMS (!), that is <λ/5000. Of course, this comes at a higher cost (atom-by-atom removal is very slow), and even worse, it is limited in the types of coatings it can handle: most of the UV coatings for instance involve fluorides which dissociate when sputtered. In this case, e-beam is the only option.

Coating types comparison

We will provide here a brief description of the choices one has to make when choosing its coating type.

Anti-reflective coatings

• Broadband vs damage threshold: since broadband generally means multi-layer coatings, the more broadband a coating is, the lower its damage threshold and the higher its price. Broadband coatings also show the property to be less sensitive to angle of incidence than other anti-reflection coatings, which makes them valuable when the optics has to be tilted over the course of an experiment for instance. Broadband coating also show lower reflectivity than single layer or V-types coatings.
• Single-layer vs V-types anti-reflection: Single-layer is more durable than V-types (which are multi-layers), and are enough to lower the reflectivity of BK7 from 4% to about 1.3%. On high refractive index materials (sapphire, Nd:YAG, ruby), single layer coating can go as low as 0.25% reflectivity at normal incidence. V-type coatings, AKA narrowband anti-reflection coatings, are best suited for laser application, since they can show reflectivities lower than 0.25% on common lens substrates.

Mirrors and partial reflectors

• Broadband vs reflectivity: generally speaking, the more broadband, the lower reflectivity and the lower damage threshold. For very broadband mirrors requirements with more than 1 µm bandwidth, the only solutions available are the metallic coatings. Bare aluminium for instance has >86% reflectivity from 200 nm to well over 20 µm
• Working in transmission requires a partial reflector. This is used for instance to sample 1% of a beam for diagnostic purposes. Mirrors are not suitable because their back face is generally uncoated with non laser polishing. Beamsplitters can also do that job.
• Incident polarisation plays an important role in how well a mirror performs. Although mirror are tuned for a specific polarisation and angle of incidence, some configurations are physically limited. Best results are achieved when used at an angle with S polarisation or at normal incidence. At equivalent coatings, a mirror tuned for P polarisation at 45° incidence can hardly achieve less than 2% loss in reflectivity compared to its S equivalent. Sometime the loss is even much higher

Filters

• Filters for fluorescence: the main issue with fluorescence is to separate the excitation light from the usable signal. Although both are generally far from each other in terms of wavelength and a sensible set-up would use the fluorescent light on a different optical axis than that of the excitation light, fluorescence is generally a low-light measurement. As such it is necessary to have the best achievable transmission at the wavelength of interest. We would generally advise a minimum blocking OD of 3 and a minimum transmission of 80%. Bandwidth and cut-off steepness are of lesser importance provided the excitation wavelength is in the blocking range.
• Raman spectroscopy can be considered as a demanding application, because of the weakness of the signal and specially because of its spectral closeness to the excitation wavelength (typically ~10-50nm, sometime as far as 100nm). Therefore we would generally advise to go for high quality filters, such as those made using ion-beam sputtering. This can produce filters with transitions of ~3-8nm. There are four basic types of filters to choose from: Long-Wave-Pass (LWP) Edge Filters, Short-Wave-Pass (SWP) Edge Filters, Notch Filters, and a Laser-Line Filters. Laser-Line Filters will transmit only the excitation light (less noise), and Notch Filters are an obvious choice for blocking the excitation line. In systems using these two filter types, both Stokes and Anti-Stokes Raman scattering can be measured simultaneously. However, in many cases Edge Filters provide a superior alternative for both Transmitting and Blocking filters. Edge filters offer better transmission, higher laser-line blocking, and the steepest edge performance to see Raman signals extremely close to the laser line.
• Broadband attenuation is easily achieved using a ND filter (Neutral Density). Those filter have an uniform spectral response (typically over 400-1200nm) but are limited in the amount of power they can handle (typically less than a few watts). Higher powers require a partial reflector. They are extremely useful for photography and to measure some light with a low damage threshold instrument. They are normally defined by their OD (optical density) value: their transmission on a scale from 0 to 1 is equal to 10^-OD. For instance a ND filter with an OD of 3 will transmit 10^-3=0.001, which equals 0.1%.

Beamsplitters

• Wavelength separation / mixing: a beamsplitter can be used to separate or mix beams at different wavelengths. In this case they act as a mirror at one wavelength and as a window at the other wavelength. When building a system that involves wavelength separation, one must pay particular attention to its own design choices: physical laws limit what is achievable with a beamsplitter. When spectral purity at a wavelength is most important, it is better to transmit this wavelength and reflect the others. If getting as much light as possible at a wavelength is the main target rather than cleaning the spectrum, then it is better to reflect that wavelength and transmit the others. Finally, control of the polarisation is important when working at 45°. Best results are achieved when reflecting S polarised light and transmitting P polarised light. Good result are achieved when reflecting and transmitting P polarised light. Other combinations must be avoided if possible, the worst one being reflecting P and transmitting S.

A step towards the future?

Last year, a group of researcher^[1] at the Rensselaer Polytechnic Institute in Troy, N.Y., reported achieving broadband virtually reflection-free anti-reflection coating using oblique-angle deposition. This coating results in a thin-film of nanorods, which grow by themselves. Self-organisation of the nanorods is obtained by tilting the substrate during the coating process. This technique is also susceptible to increase highly reflective coating to near 100% reflectivity. If this finds its way to production, the market is likely to be huge.

Reference
1. Xi, J.-Q., Martin F. Schubert, J. K. Kim, E. Fred Schubert, Minfeng Chen, Shawn-Yu Lin, Wayne Liu, and Joe A. Smart “Optical thin-film materials with low refractive index for broadband elimination of Fresnel reflection” Nature Photonics 1, 176 (March 2007)

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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

The aim of this project is to explain how to use optical technologies to solve common problems. Additionally, I will help you to understand the optical technologies available on the market.

Some tools and reference documents will also be available soon.

I hope you will find some information useful, and do not hesitate to contact me.