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, 6 by 9 inches, hardbound, 500 pages,
38 photographs, 195 drawings and CD with software, $39.95.
ABOUT THIS BOOK AND SOFTWARE PACKAGE
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 184.108.40.206 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. (A version of RED_FRINGE saved in the Excel 2010 version of the application is also provided in the book CD.)
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 220.127.116.11 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 18.104.22.168 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.
Chapter 1 is a nuanced exploration of the advantages and disadvantages of optical testing methods available to the amateur. Knowing the strengths and weaknesses of available testing methods is a definite benefit for deciding which method is appropriate for the particular job a hand.
Chapter 2 explores the optical phenomena of interference and how a probe beam of light and a reference beam can be derived and interpreted from a coherent source light beam.
Chapter 3 reviews interferometer types useful for optical testing purposes.
Chapter 4 discusses the concept and practical methods of achieving measurement accuracy. It shows how to confirm the quality of your interferometer optics through verification with out having to resort to costly standards. Included are accuracy requirements for image capture, random errors, sampling issues, noise and sensitivity variations.
Chapter 5 considers air turbulence, test stand effects, measuring astigmatism, retrace and design residual wavefront errors, vibration and enhancing fringe contrast.
Chapter 6 shows how to image the fringe pattern and construction of mounts and the optical bench interferometer.
Chapter 7 is a practical introduction to the characteristics of lasers and how they impact interferometry.
Chapter 8 explores the waveforms produced by an optical interferometer and how they can be interpreted.
Chapter 9 describes how to build a spherical-wave Twyman-Green form of interferometer, the Williams, that is compact, easy to set up, align, verify optically, and to understand.
Chapter 10 shows the construction of a Bath interferometer that is very compact with a 12 or 15 mm beam splitter cube, 6 mm ball lens and a diagonal mirror and possibly a relay lens. This device is usually best for testing slower mirrors.
Chapter 11 provides practical step-by-step guidance on how to align both the Williams and Bath interferometers. Finding the tiny returning beam can be a trying “first experience”; this chapter will show you the clever ways to track it down quickly.
Chapter 12 deals with capturing the interference pattern produced by the interferometer. Included are such things as image scale considerations, types of cameras, exposure and issues associated which processing interferograms.
Chapter 13 covers interferogram analysis and detailed instructions on how to use the software included with this book on a CDROM. Also included are sample images and worked examples of those images for the reader to practice on. There is no need to build your own interferometer before you actually process interferograms!
Chapter 14 provides insights on advanced forms of interferogram analysis and a discussion of performance prediction.
The book concludes with a Glossary, six appendices and index.
ABOUT THE AUTHOR
Bill Zmek became fascinated with astronomy and telescopes as a boy living in the plains of Nebraska. He ground and polished his first homebuilt telescope at the age of 12, using an Edmund Scientific kit and Sam Brown’s “Homebuilt Telescopes” as his guide. After perhaps two dozen mirrors, Bill’s final effort was a fourteen inch f/3.9 Newtonian, which is now a Cassegrain, and his workhorse telescope.
As an optical systems engineer, Bill has had the good fortune to have worked on a variety of space astronomy missions. For the Space Astronomy Laboratory at the University of Wisconsin, he executed the optical alignment of the High Speed Photometer, one of the original axial science instruments for NASA’s Large Space Telescope project, soon to be renamed the Hubble Space Telescope. Bill also led the optical integration of the Wisconsin Ultraviolet Photo-Polarimeter Experiment, one of three ultraviolet telescopes co-mounted and co-aligned into a Space Shuttle-borne astronomy payload known as ASTRO. This payload was first flown in 1990. After moving to Connecticut, Bill worked on the Chandra X-ray telescope optics production team as systems engineer responsible for image quality prediction, and served as systems engineering co-manager for the optical refurbishment of the HST Fine Guidance Sensor returned from the HST in the 1999 Servicing Mission 3A. After refurbishment, the sensor was re-installed into the HST during Servicing Mission 4, conducted in 2009.Bill has designed and fabricated several interferometers and other forms of wavefront sensor in the course of his work as an optical system engineer. Bill maintains an interferometric testing station in his basement