Peak-to-valley Vs RMS

[hmtad name=”Adsense Unit 2″ align=”center”][hmtad name=”Adsense Unit 2″ align=”center”]What is an optic surface figure?

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.

SURFACE FLATNESS (PEAT-TO-VALLEY) QUALITY APPLICATIONS
less than λ/2 very low non critical divergent applications only
λ/4 low Often best standard for cube beam splitter. Not suitable for high power applications or when wavefront control is important
λ/10 good General standard for quality manufacturer. Suitable for most laser and scientific application.
λ/20 very good Manufacturers who specify surface flatness in peak-to-valley advise this flatness for critical wavefront control applications such as interferometry or intense femto-second lasers. But honestly, if this is your case you wouldn’t want to leave room for imprecision, and you would choose a manufacturer able to specify the RMS flatness.

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.

SCRATCH-DIG QUALITY APPLICATIONS
60-40 Very low Commercial grade, non-critical applications. Also used in low power laser and imaging applications where scattered light is not as critical as costs.
40-20 Low Standard scientific research applications, for laser or imaging applications with focused beam that tolerate little scattered light.
20-10 Moderate Laser mirrors and extra-cavity optics. For laser and imaging application with focused beams where minimising scattered light is important. This is the best quality offered by some manufacturer.
10-5 High Intra-cavity laser optics, high power applications.

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