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Top = > Essays=20 On Optics > Defining Apochromatism=20 =

Defining=20 Apochromatism
by Thomas Back=20

Updated 6-29-03=20

With the proliferation of apochromatic refractors = that are=20 available to the amateur astronomer, it is time to = define the=20 parameters of a true apochromatic objective lens. The = modern=20 definition of "apochromat" is the following: An = objective in=20 which the wave aberrations do not exceed 1/4 wave = optical path=20 difference (OPD) in the spectral range from C (6563A - = red) to=20 F (4861A - blue), while the g wavelength (4358A - = violet) is=20 1/2 wave OPD or better, has three widely spaced zero = color=20 crossings and is corrected for coma.=20

Here is a more detailed analysis for those that are = interested. The term "Apochromat" is loosely used by = many=20 manufacturers and amateurs astronomers. Let's look at = the=20 history of the definition, and maybe a more modern = one. Ernst=20 Abbe, in 1875, met and worked for Carl Zeiss, a small=20 microscope, magnifier and optical accessory company. = They=20 realized that they needed to find improved glass = types, if=20 they were going to make progress with the optical = microscope.=20 In 1879, Abbe met Otto Schott. Together they introduce = the=20 first abnormal dispersion glasses under the name of = Schott and=20 Sons. Abbe discovered that by using optically clear, = polished=20 natural fluorite, in a microscope objective, that=20 apochromatism could be achieved. These first true = apochromatic=20 microscope objectives were so superior to the = competition,=20 that Zeiss gained nearly the entire high end market. = So secret=20 was the use of fluorite, that Abbe marked an "X" on = the data=20 sheet for the fluorite element, so as to keep it = secret from=20 the other optical companies.=20

Abbe's definition of apochromatism was the = following.=20 Apochromat: an objective corrected parfocally for = three widely=20 spaced wavelengths and corrected for spherical = aberration and=20 coma for two widely separated wavelengths. This = definition is=20 not as simple as it sounds. I have designed thousands = of=20 lenses: simple achromats, complex achromats, = semi-apos,=20 apochromats, super-achromats, hyper-achromats, and = Baker=20 super-apochromats. Abbe's definition, to put it in = clearer=20 terms (I hope) is that a true apochromat is an = objective that=20 has three color crossings that are spaced far apart in = the=20 visual spectrum (~4000A, deep violet to ~7000A, deep = red).=20 However, just because a lens has three color = crossings,=20 doesn't mean that it is well corrected. Let's say that = a 4"=20 lens has three color crossings at the F, e and C = wavelengths=20 (4861A, 5461A and 6563A). Fine, this objective is now=20 considered an apochromat by most amateurs and even = optical=20 designers because it has three color crossings in the = blue,=20 green and red -- the common definition of an = apochromat. But=20 what about the levels of spherical aberration at each = of these=20 wavelengths? If the lens is 2 waves overcorrected at = 4861A,=20 and 1.5 waves undercorrected at 6563A, is it still an=20 apochromat? No. It is no better than an achromat, as = the OPD=20 wavefront error is worse than a 4" f/15 achromat.=20

Abbe, in his definition of apochromat, states that=20 spherical aberration must be corrected for two widely = spaced=20 wavelengths. Now I will tell you what happens when you = correct=20 spherical for two widely spaced wavelengths: you = correct for=20 all the wavelengths between them too. This is called=20 correcting for spherochromatism (the variation of = spherical=20 aberration with a change in wavelength). Only with = extremely=20 long focal lengths, advanced Petzval designs, = aspherics, large=20 air spaces, or a combination of these designs/factors, = can you=20 correct for this aberration. It is the designer that = must come=20 up with a good compromise of color correction, lack of = spherical aberration (3rd order and zonal) and = controlling=20 spherochromatism, so as not to degrade the image = contrast. Al=20 Nagler uses a wide air-spaced Petzval design with = Fluorite and=20 an exotic glass in his top of the line apochromats to = control=20 the above aberrations. Takahashi's latest ED apo = triplets use=20 a large air space. Roland Christen (Astro-Physics) = uses a very=20 high quality super ED glass (FPL-53) and specially = matched=20 crowns to control the various aberrations (he also = slightly=20 aspherizes the outer surfaces). TMB Optical uses = Russian OK-4=20 super ED glass (similar to FPL-53) with an outer crown = and a=20 special dense crown glass, using air spacing with = different=20 internal radii, and hand figuring to control these=20 aberrations.=20

Also, the Abbe condition of coma correction is = overstated,=20 that is, if a lens is well corrected for coma at one=20 wavelength, in almost all cases it will be corrected = for coma=20 at all the visual wavelengths. Now you might ask, = after all=20 this, just what is a modern definition of = apochromatism? Well,=20 as you read, it is not only three color crossings. One = of the=20 first things an optical designer discovers is that = with=20 catalog glass data, it is easy to design lenses with = three or=20 even four color crossings (super-achromat). But when = you get 6=20 place data, these designs often breakdown to only two = or three=20 color crossings (that is not to say that a 4 color = crossing=20 objective cannot be made -- it can), albeit with the = chromatic=20 focal shift being very small. What is really important = is how=20 small the chromatic focal shift is (not the zero = crossings)=20 over a wide spectral range, and how low the spherical=20 aberration is over that same range. So we are left = with an=20 ambiguous definition.=20

After designing, testing and selling many different = apochromatic lenses I can state this: There is no = "definite"=20 line where a lens becomes "apochromatic" in the world = of=20 commercial apochromatic lenses.=20

But any lens, be it a doublet, triplet, quad, = air-spaced or=20 Petzval, that has a peak visual null (~5550A - the=20 green-yellow) with a Strehl ratio of .95 or better, = coma=20 corrected and is diffraction limited from C (red) to F = (blue)=20 with 1/4 wave OPD spherical or better, has good = control of the=20 violet g wavelength with no more than 1/2 wave OPD P-V = spherical and optical spot sizes that concentrate the = maximum=20 amount of photons within the diffraction limit -- a = result of=20 the low spherical aberration, which can be seen with = modern=20 optical design programs, as the "spot rays" will be = seen=20 concentrated in the center of the spot, not evenly or = worse,=20 concentrated outside the center -- will satisfy the = modern=20 definition of "Apochromatism."=20

Lenses of this quality do not satisfy the Abbe = definition,=20 but for all intents and purposes, will be color free = and will=20 give extremely sharp and contrasty images.=20

Thomas M. Back
TMB Optical =

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