interferometry for Amateur Telescope Makers

interferometry for Amateur Telescope Makers

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Interferometry for Amateur Telescope Makers, A practical guide to building verifying and using an optical interferometer including powerful software to evalute interferograms

By William Zmek.

Product Information: 6 by 9 inches, hardbound, 500 pages, 38 photographs, 195 drawings.

This book has been written for the Amateur Telescope Maker (ATM) one who grinds, polishes, figures and tests optical surfaces with the objective of achieving near perfection and desires a practical guide to testing and interpreting full-aperture optical interferogram using a homebuilt interferometer. To that end, I start with a review of optical interference, after which I provide a systematic approach on how the ATM can build an optical interferometer without any input other than this book and homemade, surplus or common off-the-shelf components. For the Williams interferometer the experienced telescope maker is likely to have accumulated a well-stocked ???Junquebox??? that could be a significant component source. However, the main components if purchased today (Summer 2017) cost less than $300: He-Ne Laser $69.95 and power supply $11.95, 30mm cube beam splitter $39.95, GRIN lens $47.50 or 8.0mm ball lens $29.95, reference optic $26.00, Webcam $25.00 and auxiliary webcam lens $49.50. See Appendix D or a list of suppliers. This book describes how to make mounting hardware for little more than the time and effort it takes to build them but if purchased new or even used these would be a significant additional expense.

The accuracy of the interferometer can be easily confirmed using a spherical mirror that has been validated by a go/no-go Foucault knife-edge (KE) null test. Spherical mirrors are relatively easy for the ATM to make and null test to a high level of accuracy. In Section 1.4 I note that the accuracy of a concave sphere that appears uniform and velvety smooth in the Foucault null test can be assumed to approach a smooth 1/40 wave peak-to-valley surface. And in Section 4.2.1.1 it is observed that a four-inch diameter sphere of sixteen inch radius will allow verification of mirrors as fast as f/2 at infinity focus. This test sphere need not be aluminized. In fact it is normally better that it is not. To close out the book, I offer some words on how to fold the rating of the objective mirror into a more complete perspective on the performance of a finished telescope.

The fringe following software offered with this book comes in two parts, a stand-alone executable named FRINGE_DAT, and an Excel 2003 spreadsheet program named RED_FRINGE. The former collects fringe center data from an interferogram, and the latter processes that data into information about the tested mirror. The program is designed to make the data processing and analysis relatively easy and quick and provides features that allow whole system assessment by inclusion of secondary mirror error and on-axis eyepiece primary spherical aberration.
The choice to program in Excel ??? which was made so that the formulas and computations could be accessed by the interested user ??? was perhaps a bit risky, in that many readers will not own a copy, and also because software applications like Excel suffer periodic alterations by their suppliers, thereby making the specifics of menu trees and procedural details provided in this book prone to obsolescence. However, because the capabilities offered in applications such as Excel are usually simply added upon rather than replaced with different capabilities, the user of RED_FRINGE having a later release of Excel than the 2003 version will only need to search within the menus for the new location of any particular tool or widget mentioned in Chapter 13. The software should still work fine. 

Two types of interferometers are discussed in detail: The Williams and Bath. My homemade Williams, in combination with the data reduction software that accompanies this book, produced test results for a particular six-inch diameter f/8 mirror that are near-identical to that found by a state-of-the-art heterodyne interferometer with its sophisticated software (see Appendix C). Also included with this book are the digital images used to measure the mirror so that readers can ???reduce data??? even before they have constructed their own interferometer.

The advantages of a carefully executed, full-aperture interferometry test is that it provides a densely sampled measurement of every possible significant form of optical error. On the other hand, the ATMs standby tool, the knife-edge test provides only partial visibility into the mirror???s full surface figure. The use of ???no- mask??? digital image KE tests avoid the accuracy-degrading effects of diffraction that accompanies the visual Couder mask test, by eliminating the vagaries of shadow cutoff estimation (except at the very edge of a tested mirror). These tests also replace the subjective estimate of Foucault shadow depths with true measurements based on the modern silicon detector array such as the CCD. Even so, this form of the test only measures axisymmetric components of the surface error, and still only measures across a single diameter of the tested mirror. Interferometry can easily assess all forms of error in an optic, and does so across the entire surface, not just a single diameter. The knife-edge mask test always under-reports the departure of the actual surface from the ideal surface. In other words, the knife-edge test overstates the actual surface accuracy. Normally this departure is not significant for smooth, slower, moderate aperture mirrors. However, for thinner, faster and larger mirrors the differences can be significant. For a variety of reasons the trend in telescope construction today is toward much faster, larger thin-mirror telescopes.

The careful reader will perhaps wonder if the in-depth error analysis provided in Section 13.4.1.1 implies that interferometry is more sensitive to set-up tolerances and mirror geometry measurement tolerances than the Foucault-Couder Mask test. Not at all ??? those same sensitivities apply exactly to the Foucault mask test. Tolerance error in the measurement of the mirror ROC and diameter apply equally to both tests. For more information, consult Section 13.4.3.2 for similarities and differences between the Foucault result and interferometric results.

Almost every ATM is familiar with the extreme accuracy capabilities of an optical laser interferometer but most never attempt to unleash its power in their shop because it is seen as difficult to construct and master in use. The repeatability of an interferometric measurement as shown in this book is generally commensurate with that of a well-executed Foucault mask test. Interferometry can claim much higher accuracy than the K-E test due to its ability to sense the entire surface of a tested mirror in a single image, and in its ability to sense all of the error present in that surface. Recall that the K-E test cannot. This reality is covered in detail in the earlier pages of this book. The purpose of this book is to demonstrate how any careful worker???a characteristic of every serious ATM???can master and exploit the power of optical interferometry.