Optical Talk...

We've written several articles on telescope optical fabrication and optics, which have appeared in well-known amateur-oriented publications, such as Amateur Astronomy (http://www.amateurastronomy.com/). The thrust of these articles has been to point out the importance of careful adherence to a tolerance. Many opticians effectively do not use a tolerance, although they frequently quote adherence to the "1/4 wave Rayleigh criterion." They also state that 1/4-wave is diffraction limited, whereas the Millies-LaCroix criterion better satisfies the definition of diffraction-limited. Lord Rayleigh made reference to a point at which aberration, from all sources, begins to become troublesome, and that happens to be 1/4 wave at the wavefront. 1/4 wave peak-to-valley, also expressed as 1/13 wave RMS, does not focus the maximum possible energy within the diffraction spot, and will effectively create a diffraction disk 2.5X the size of that of a Millies-LaCroix-conforming mirror. Incidentally, the Millies-Lacroix tolerance results in a minimum 1/8-wave accuracy at the wavefront, or about 1/25 wave RMS. We considered using other forms of test, including autocollimation null test with a flat, Ronchi test in various forms, and interferometry. We did not adapt any of these test for several reasons: For one thing, the error of measurement depends on the sum of the error of the auxiliary components, such as flats, reference elements, null lens, and component spacing. Without sophisticated and incredibly expensive error compensation, these methods did not begin to approach the knife-edge test in the form in which we implement it, and are not inherently quantitative for purposes of measuring and certifying wavefront error. The theory which we apply to optical data test reduction is the same as that described by Texereau in "How to Make a Telescope" and as discussed by R. Suiter (author of Star Testing Astronomical Telescopes) in various articles on the subject. The signed test report, which you will receive with your mirror, will include wavefront P-V, RMS, Strehl ratio and diffraction disk Relative Transverse Aberration. Using the data provided, any amateur mirror maker will be able to reproduce the conditions of test and validate the test report results provided with the mirror.

A comment on our F/6 Focal Ratio Mirrors; The F/6 focal ratio, with its more lenient tolerance, not only makes it feasible to routinely achieve a higher 1/20th wave rating, but the steeper light cone is more easily tolerated by most eyepieces that are traditionally used for planetary observing. Although we believe that "bigger is better" when it comes to aperture, we also realize that some observers prefer a smaller aperture with long f-ratio, with its ultra high quality, APO-refractor-like images, because it is also more portable, and does not require a high ladder to get to the eyepiece. If you do not mind the minor logistic compromises needed to transport and use a larger telescope, we believe that larger aperture will reveal more detail. This is because the physics of optics dictate that resolution, and therefore visual information, is increased in direct proportion to the aperture.When you factor in the additional light grasp (proportional to the square of the aperture) with which the additional visual detail is illuminated in a larger aperture, the impact of larger aperture is dramatically compounded. As you can see, there is a tradeoff in terms of convenience, preferred observing pursuits, and budget as well. If you wish to discuss these issues to determine what Lightholder mirror to get, or what telescope to build, please feel free to contact us by e-mail, regular mail or phone. In order to optimize the view and resolution capacity of your telescope, you must be able to magnify the image enough to have a 1mm exit pupil, which is over 250X for a 10", and 400X for a 16" mirror.

"Our concern for your mirrors quality does not end with the figure on the primary". Optical excellence, performance and durability depend on the coating on the primary mirror as well. For that reason, we have selected Spectrum Coatings to do all our coatings, using their Ion-Assisted Deposition (IAD) process that is the most advanced commercial coating available today, yielding the smoothest, densest and most compact oxide deposition. The coating has a durable quartz overcoat, SiO2 that is superior to the prevalent SiO, silicon monoxide overcoat. You are assured that your mirror's figure will be matched by a coating that will be the best and most durable currently available for telescope mirrors. For more extensive information on the IAD process, see "http://www.spectrum-coatings.com"


Optical Quality Standards:

Various criteria are used to determine and state acceptable optical quality and include:

Rayleigh Criterion:

The total wavefront error, peak-to-valley, must not exceed 1/4 wavelength of yellow-green light or the image will noticeably degrade. This tolerance is very well known and is frequently and mistakenly confused with the term "diffraction limited". Conventionally, some people also use the 1/4 wavelength expression to be synonymous with diffraction-limited, which it actually is not in most cases. The problem with the Rayleigh tolerance, especially when it is not mathematically qualified, as in its RMS equivalent as to extent of area on the mirror, is that it means different focus capability for different mirror sizes and f-ratio combinations. Still another is that 1/4 wave of variation on a mirror with a "sawtooth" wavefront shape, can vary from nearly 1/8 wave RMS to nearly 1/16 wave RMS. It may or may not satisfy the Marechal Criterion, so is fairly indiscriminate.

Marechal Criterion:

This is another way of expressing the Rayleigh tolerance in root-mean-square (RMS) terms. It is more stringent than the Rayleigh Criterion, because it rejects mirrors with sharp slopes having 1/4 wave p-v variation. The Root Mean Square is basically the square root of the averaged deviations squared, which is equal to the standard deviation of the errors measured at various radii slope and zones. 1/4 wave (5.5 millionths of an inch) of spherical aberration on average translates to 1/13.4 wave RMS. An RMS rating divided by 3.35 gives an equivalent peak-to-valley wavelength rating for optics with smooth variations, e.g., smooth undercorrection. 1/27 RMS, the Marechal equivalent for the surface, is equivalent to (27/3.35=8.05) 1/8.05 surface p-v. At some size/f-ratio combinations, optics conforming to the Marechal, direct all the light from a star within the star image (or diffraction disk), but at other combinations, (particularly large, fast mirrors) it forms a blur spot larger than the size of the star image. As a footnote, in the opinion of the author, it should be stated that any attempt to compare the performance of different diameter/f-ratio combination using their wave ratings, even if the wave ratings are accurately calculated, is a difficult process and not straightforward.

Danjon-Couder Conditions:

This two-part optical criterion, which defines a totally acceptable optic from the standpoint of its ability to focus in two ways, states that the mirror must be near-diffraction-limited and also meet the Rayleigh or Marechal tolerance, stated as follows: 1. Over the greatest part of the aperture, the wavefront has a mild slope and on average the transverse aberrations should not exceed that of the diffraction disk. (NOTE: This does not mean the mirror has to be diffraction-limited across its entire aperture to meet the D&C criteria.) 2. The Rayleigh 1/4-wavelength tolerance is everywhere obeyed, and over most of the aperture, deviations should be appreciably less. (E.g., Marechal Criterion.) This dual criterion is generally speaking less stringent than diffraction-limited. Contrary to common belief, part 1 of this criterion is not identical to diffraction limited. Note the part of the statement above, i.e., "on average, etc." These conditions must be simultaneously satisfied at a position of average focus.

Diffraction limited:

This refers to the ability of the mirror to aim its light within the boundary of the diffraction disk formed by the mirror/f-ratio combination being considered. The degree of conformance to diffraction-limited condition is typically expressed in Relative Transverse Aberration (RTA) using Texereau's method, normally used with knife-edge estimation. This is a figure obtained by a calculation, where the blur spot size produced by the mirror, is divided by the theoretical diffraction disk size calculated for the aperture. A ratio of 1.0 or less is diffraction-limited, and the smaller this ratio is, the better the mirror's figure and resulting wavefront is. Ratios of less than 50% are extremely hard to measure and are therefore approximate. The Millies-LaCroix tolerance, which is applied to knife edge testing, provides a tolerance on the surface of the mirror, which when attained during figuring, assures the mirror's light will be aimed at the diffraction disk with an RTA of 1.0 or less. This will provide as precise a focus as optical theory will allow, ie. 84 % of the light into the disk for an unobstructed aperture, and the remaining light will propagate outward in the diffraction "rings". The term "diffraction limited" is an absolute, relevant indicator of optical accuracy on the primary's surface. It does not, however, relate directly to surface large- or small-scale roughness, or figure of revolution error. Large- or small-scale roughness on a mirror which is otherwise measured as having a satisfactory RTA will nevertheless propagate some of the impinging light outside the diffraction disk. Normally, but not always, a mirror that is diffraction-limited across its entire diameter is more accurate than 1/4 wave.


Tests and their merits:

An optical test should be designed to accomplish two objectives, the first of which is to provide data to the optician to make corrections during the figuring process, and the second of which is to make an educated guess how accurate the completed mirror is and/or predict how well it will perform under conditions of use in the telescope. It is desirable (although not necessary) that the method used to determine figuring correction strategy will be the same as that used to assess performance, e.g., to certify the optics for a purchaser. Finally, depending on the criteria used by the optician, the tests should be quantitative enough to define the attainment of the diffraction limit, and/or the amplitude of defects at the wavefront, as recommended by Jean Texereau in the book How to Make a Telescope. The tests most commonly used in commercial facilities consist of one of the following or a combination of them.

Knife-Edge or Foucault Test:

Hereafter we'll refer to this as "knife edge" test, which is conducted at Center of Curvature (COC). This test by far is the most used by the amateur telescope maker and has numerous applications among professionals. It's sensitive and proven to be reliable and simple to perform. Its drawbacks include: it requires practice to develop the skills necessary to interpret mirrors with tight tolerances; shadow contrast is subjective and creates an inevitable error of estimation. Its primary drawback is that it is a "two-dimensional" test, and does not readily detect astigmatism or errors in figure of revolution ("out of round" errors). It is difficult to determine which zones, or ring-shaped areas on the mirror, are relatively high or low, and this requires considerable skill on the part of the person performing the test. Also, many amateurs claim the data reduction is tiresome and it requires the building of an "elaborate" knife-edge tester. Fortunately, with practice, the accuracy of the data reduction can be reliable, and with computer programs such as ADMIR, TEX, etc., very fast and convenient. And, an accurate tester with vernier movement is really not all that hard to make, and satisfactory prefabricated testers are commercially available at reasonable price. The knife-edge test, if rigorously applied, can determine conformance to diffraction-limited criteria and amplitude of wavefront defects. It is a quantitative test and also yields an excellent visual, qualitative picture of surface roughness in the form of "dog-biscuit" (large scale roughness), "lemon peel" (microfinish roughness), or other residual artifacts such as figuring sweeps from sub-diameter tools. Data produced by the test can easily be double-checked independently at little expense, with a relatively more restricted level of skill than that possessed by the person who did the figuring. (Measuring a mirror involves less skill than figuring.)

Null testing:

In this test, either a full-size flat or a lens is used to provide a collimated exit beam with negative and opposite spherical aberration from the mirror, to balance the primary's spherical aberration. When the returning, reflected beam is cut with a knife-edge or Ronchi grating, the returning beam will show an even graying, or "null" (thus the name of the test) of a perfect surface under test, and opposing areas of shadow/brightness at radii having high or low zones in an imperfect optic. (With the Ronchi grating, the vertical lines will display bowing or pincushion in the high/low zonal areas.) It is quite obvious from the shadows which areas are high or low relative to the desired parabola, unlike the knife-edge. Theoretically all the optician need do is work the high zones displayed by the null test until the mirror nulls equally when the returning light cone is cut by the knife-edge, or the Ronchi lines are perfectly straight. Reference surface errors, i.e., high or low zones on their glass, compound any existing errors in the mirror under test. Typical errors in test elements are 1/10 - 1/20 wave. There are many variations in the null test depending on auxiliary optics and their configuration, although the primary and most common arrangement is a full-diameter optical flat in the Double-Pass Null test, and the lens-based tests, which use a lens to introduce an equal, and opposite spherical aberration to that of the optic under test. These include the Dall test, the Offner and the Ross compensating lens systems. Besides the error, which the auxiliary lens or mirror optics contribute to the test, another potential source of error is spacing errors and component arrangement, which can have a drastic (and negative) effect on accuracy. The null test in all its forms is not inherently quantitative. It is superior to the Foucault test in terms of 3-dimensional views of the mirror. It is almost equally as discriminating of surface roughness as the knife-edge test. Focograms and/or Ronchigrams can be photographed and supplied to support test reports substantiating mirror conformance, and the optician can use mathematical interpretation to estimate error height. It is extremely difficult or expensive to produce an accurate null for a large parabola because of the cost and difficulty of fabrication of the flat or null elements, therefore most ATM's will not be able to double-check test results supplied, using a null procedure of their own construction.

Ronchi test:

This test is very attractive for limited, specialized use, as there is normally not any data reduction or interpretation involved. The Ronchi grating typically consists of a photographically produced set of alternating dark and transparent lines on a photonegative. It can be used at the COC in place of the knife-edge, or at the null point of a null test. When mounted in an eyepiece in place of the lens, and used to view the image of a star at focus, it's a null test for a parabola. However, at best most authorities agree it is not sensitive enough at the focus of a telescope to discern an excellent mirror from one that's merely adequate, nor is it appropriate to be used for figuring purposes in the scope due to turbulence. Its best attribute is in seeing a rolled edge, although the observer cannot easily determine how severe or exactly how wide the rolled edge is. Most experienced star Ronchi testers recommend 100 - 133 lines per inch, adjusting focus so that 3 - 4 bands are visible across the mirror's image. When used with null testing during mirror figuring, there are conversion methods, which can convert divergences from a straight line on the bands into absolute error, and thereby estimate the height of defects at the null wavefront. By itself, the Ronchi test is not quantitative, cannot establish absolute error, or conformance to any of the standards/criteria discussed above.

Interferometer:

Light's wave nature is revealed in the interference fringes produced by superimposing a mirror's and reference surface's wavefronts in the same space. It's been frequently said that interferometry "Takes no Prisoners," and to some extent this is so, especially when it comes to assessing the entire surface in a 3-dimensional way that reveals out-of-round errors which can surpass peak-to-valley errors in magnitude. Although this test is sensitive, its accuracy is dependent on the reference, auxiliary optics and the overall set-up. Paraphrasing a known authority on interferometry, all the components within the interferometer cavity contribute their error, and the interferometer tests its own components in addition to the test mirror. Normally, when an extremely good mirror is checked by an interferometer, I believe it will be estimated as worse than it really is due to internal error accumulation. Typical reference element errors are on the order of 1/10 - 1/20 wave. It's also costly and not likely to be used by an amateur to test only one mirror. With the aid o f computers it does allow a graphical interpretation of the surface showing large-scale roughness and zones better that other tests (seeing is believing). Interferometry is extremely sensitive to spacing of reference elements, and slight inaccuracy in this spacing can grossly affect estimations resulting from this test. Using computer integration software, just about every form of optical aberration can be displayed and enhanced to provide a clear picture of quantitative effect. The program can typically estimate degree of conformance to a diffraction-limited tolerance, e.g., Strehl ratio, and various forms of wavefront error, such as rms, p-v, etc. Few people have the capability to replicate an interferometric test, and with the computer programs typically used in conjunction with the test costing many thousands of dollars, few can afford to. The most accurate interferometers are common-path interferometers and other commercially produced brand-name devices costing over $100,000.

Star test:

This test is fairly easy to do and only requires your eye and an eyepiece as the primary instruments. It is very sensitive and almost a null test for a parabola so there is no reduction of data to deal with. It is also a "learned test" and is subject to interpretation. It tests the atmosphere, primary and secondary mirrors, collimation of the optics and eyepiece and eyeball combination. A good atmosphere is a requirement for a valid test. It shows qualitative spherical aberration and astigmatism at a glance. Good atmospheric steadiness is required to detect zones and other defects clearly. Surface roughness, both large- and small-scale, is disclosed by the star test. Anyone can do this test, but it is not inherently quantitative. Some quantitative measurement can be made of wavefront error if a 1/3-aperture mask is placed behind the secondary mirror in a Newtonian (or in front of the lens in a refractor). The ratio of the distance of focus knob travel from disappearance inside of focus of the diagonal's shadow to the distance of travel to re-emergence of the shadow will provide a rough estimate, everything else being equal. See R. Suiter's book, Star Testing Astronomical Telescopes.