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<html xmlns="http://www.w3.org/TR/REC-html40" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:v="urn:schemas-microsoft-com:vml"> <head><meta name="viewport" content="width=device-width, initial-scale=1"> <meta http-equiv="Content-Type" content="text/html; charset=utf-8"><meta http-equiv="Content-Language" content="en-us"> <title>Amateur Telescope Optics</title> <meta name="keywords" content="telescope, optics, diffraction, wavefront, optical aberrations, spherical, coma, astigmatism, chromatism, spherochromatism, mtf, newtonian, cassegrain, gregorian, dall-kirkham, paul-baker, off-axis, tilted, fraunhofer, achromat, distortion, defocus, central obstruction, curvature, misalignment, atmospheric turbulence, eye, eyepiece, refractor, reflector, rms, strehl, schmidt, maksutov, houghton"> <meta name="description" content="Optical aberrations in amateur telescopes. Includes principles of physical and optical imaging with detailed review of primary aberrations. Also, aberrations in popular reflecting, refracting and catadioptric telescope objectives, telescope eyepiece and human eye."><meta name="verify-v1" content="4a482o+wtY5M+rm7eB5FrDZOZ6LMk9KgcTrV+xiWJtA=" /><META name="y_key" content="9e00c71c8c8c0d28" > <style fprolloverstyle="" type="text/css">A:hover {color: #FFFFFF} <link rel="icon" type="image/x-icon" href="favicon.ico"/> </style> </head> <body alink="#D2E1F0" bgcolor="#999999" link="#CCCCCC" style="font-family: Verdana; font-size: 10px" vlink="#F9E186"> <div align="center">  <table bgcolor="#FFE066" border="0" cellpadding="0" cellspacing="0" height="770" width="800"> <tbody> <tr> <td colspan="2" height="55" style="text-indent: 21; padding-left:21px; padding-right:21px; padding-top:4px; padding-bottom:3px; border-left-style:solid; border-left-width:0px; border-right-style:solid; border-right-width:0px; border-top-style:solid; border-top-width:0px" valign="top"> <div style="border-style:solid; border-width:0px; "> <h1 align="center" style="text-indent: 0"> "袦芯卸写邪褋褍褑褉薪械褌邪褔泻械斜懈谢械锌褌懈褑械褍谢械褌褍..." (Maybe the black dots were birds in flight)</h1> Notes on AMATEUR TELESCOPE OPTICS</div> </td> </tr> <tr> <td height="75" style="text-indent: 21; padding-left:11px; padding-right:11px; padding-top:4px; padding-bottom:3px; border-left-style:solid; border-left-width:0px; border-right-style:solid; border-right-width:0px; border-top-style:solid; border-top-width:0px" valign="top" width="400" align="justify"> On an early autumn day of 1608, Hans Lipperhey, a spectacle maker from Middelburg, in the Netherlands' coastal province of Zeeland, applied before the States General of The Hague for a patent on an "instrument for seeing far". By that time, use of small rounded glass disks to aid the natural eyesight wasn't new. Those bulging out on both sides, resembling lentil - or "lens" in Latin - have been used to correct for farsightedness since the mid 13th century. The idea of a device for magnifying distant objects may have been already grasped for some time as well. But this was the beginning of something else. In the summer of 1609, Galileo, Harriot, and others, turned the new Dutch invention - the "spyglass" - toward the night sky. The telescope was born. This tale grew old, but our fascination with telescopes has not. Following text is an attempt to give more of an insight into their inner workings. More specifically, how do they form images and what factors determine their quality. </td> <td height="75" style="text-indent: 21; padding-left:11px; padding-right:11px; padding-top:4px; padding-bottom:3px; border-left-style:solid; border-left-width:0px; border-right-style:solid; border-right-width:0px; border-top-style:solid; border-top-width:0px" valign="top" width="400" align="justify"> Somewhat unusual, the main aspect is that of the optical wavefront, as opposed to the geometric (ray) "interface". That deliberate choice, while perhaps somewhat less convenient, allows for more accurate qualitative assessment, and should throw more light at the underlying physical fundamentals. Main reference sources are as follows: (1) Astronomical Optics, Daniel J. Schroeder, (2) Aberration Theory Made Simple, Virendra N. Mahajan, (3) Optical Imaging and Aberrations I and II, Virendra N. Mahajan, (4) Optics, Eugene Hecht, and (5) Telescope Optics, Harrie Rutten and Martin van Venrooij. Most of raytracing plots and routine checkups are by <a href="http://www.atmos-software.it/Atmos8_9.html" style="color: #0000FF" target="_blank"> ATMOS</a>, Massimo Riccardi, and <a href="https://www.lambdares.com/edu/" style="color: #0000FF" target="_blank"> OSLO</a>, Sinclair Optics. Most of diffraction patterns were generated by <a href="http://aberrator.astronomy.net/" style="color: #0000FF" target="_blank"> Aberrator</a>, Cor Berrevoets. For additional reading, see extensive coverage of telescope optics and related subjects at Bruce MacEvoy's <a href="http://www.handprint.com/ASTRO/ae1.html" target="_blank"> Astronomical optics</a> (descriptive), and Solo Hermelin's <a href="http://www.slideshare.net/solohermelin/presentations/3" target="_blank"> SlideShares</a> (mathematical). For related graphics, <a href="https://wp.optics.arizona.edu/jcwyant/mathematica/webmathematica/" target="_blank"> Wyant College</a> website. <script type="text/javascript">var addthis_pub="vladis";</script><a href="http://www.addthis.com/bookmark.php?v=20" onclick="return addthis_sendto()" onmouseout="addthis_close()" onmouseover="return addthis_open(this, '', '[URL]', '[TITLE]')"> <img alt="Bookmark and Share" height="16" src="lg-share-en.gif" style="border:0" width="125" /></a><script type="text/javascript" src="http://s7.addthis.com/js/200/addthis_widget.js"></script>  </td> </tr> <tr> <td colspan="2" height="55" style="text-indent: 21; padding-left:21px; padding-right:21px; padding-top:21px; padding-bottom:3px; border-left-style:solid; border-left-width:0px; border-right-style:solid; border-right-width:0px; border-top-style:solid; border-top-width:0px" valign="top"> <a name="TABLE_OF_CONTENTS"> TABLE OF CONTENTS</a>: </td> </tr> <tr> <td align="center" bgcolor="#999999" bordercolor="#FFFFFF" height="360" style="border-style:solid; border-width:0px; text-indent: 0; padding-left:11px; padding-right:11px; padding-top:10px; padding-bottom:10px" valign="top" width="400">  1. <a href="wave.htm"> IMAGE FORMATION IN A TELESCOPE</a> <a href="wave.htm#location">Rays and waves</a>  <a href="diffraction.htm"> Diffraction</a>  <a href="diffraction_image.htm">PSF</a> 1.2. <a href="reflection.htm"> Reflection and refraction</a> 1.3. <a href="system.htm"> Optical system of a telescope</a> 1.3.1 <a href="gaussian_approximation.htm"> Gaussian approximation</a> 2. <a href="functions.htm"> TELESCOPE FUNCTIONS</a> 2.1. <a href="functions.htm#1.4.1._Light_gathering_power"> Light grasp</a> 2.2. <a href="telescope_resolution.htm"> Resolution</a> 2.3. <a href="telescope_magnification.htm"> Magnification</a> 3. <a href="aberrations.htm"> TELESCOPE ABERRATIONS: Types, causes</a> 3.1. <a href="aberrations.htm#caused_by"> Wavefront aberrations</a> 3.2. <a href="ray_geometric_aberrations.htm"> Ray (geometric) aberrations</a>* 3.3. <a href="conics_and_aberrations.htm"> Conics and aberrations</a> <a href="conic_surface_aberrations.htm"> 2</a> 3.4. <a href="terms_and_conventions.htm"> Terms and conventions</a> 3.5. <a href="aberration_function.htm"> Aberration function</a> <a href="Seidel_aberrations.htm">Seidel</a> <a href="zernike_aberrations.htm"> Zernike</a> <a href="zernike_coefficients.htm"> 2</a> <a href="zernike_expansion_schemes.htm">3</a> 4. <a href="spherical1.htm"> INTRINSIC TELESCOPE ABERRATIONS</a>      4.1. <a href="spherical1.htm#specified"> Spherical</a>   <a href="spherical1.htm#to_the"> Primary</a> <a href="lower_order_spherical.htm">2</a>   <a href="higher_order_spherical_aberration.htm"> Higher-order</a>   4.2. <a href="coma.htm"> Coma</a><size="3">*  4.3. <a href="astigmatism1.htm"> Astigmatism</a><size="3">*   4.4. <a href="defocus1.htm"> Defocus</a>   4.5. <a href="distortion.htm"> Distortion</a>  4.6. <a href="curvature.htm"> Field curvature</a> 4.7. <a href="chromatic.htm"> Chromatism</a>   <a href="secondary_spectrum_spherochromatism.htm"> axial</a>   <a href="lateral_color.htm">lateral</a>   <a href="polychromatic_psf.htm"> effect</a>* 4.8. <a href="fabrication.htm"> Fabrication errors</a>  <a href="testing_optical_quality.htm">4.8.1.</a><a href="testing_optical_quality.htm"> Optical tests</a> <a href="testing_optical_quality.htm"> Double pass test</a>   <a href="testing_optical_quality.htm#prevent"> Interferometry</a>  <a href="foucault_test.htm">Foucault</a>  <a href="ronchi_test.htm"> Ronchi</a>  <a href="waineo_null_test.htm"> Waineo</a>  <a href="hindle_sphere_test.htm">Hindle</a>  <a href="dall_ross_null_test.htm"> Dall/Ross</a>  <a href="offner_null_test.htm">Offner</a> 4.9. <a href="optical_coatings.htm"> Transmission materials effects</a> <a href="optical_coatings.htm">glass</a>  <a href="optical_coatings.htm#down"> coatings</a>  5. <a href="induced.htm"> INDUCED ABERRATIONS</a> 5.1. <a href="induced.htm#environment"> Air-medium errors</a> <a href="induced.htm#surfaces.">Seeing error</a>   <a href="kolmogorov_limitations.htm"> Model limitations</a> <a href="seeing_and_aperture.htm"> Seeing and aperture</a> <a href="seeing_error.htm">The seeing Strehl, resolution, OTF</a> 5.2. <a href="turbulence_error.htm"> Low-level turbulence, tube currents, atmospheric refraction/dispersion</a> 5.3. <a href="induced2.htm"> Alignment errors</a>* 5.4. <a href="induced2.htm#3.3._Forced_surface_errors"> Force-induced surface errors</a> </td> <td align="center" bgcolor="#999999" bordercolor="#FFFFFF" height="360" style="border-style:solid; border-width:0px; text-indent: 0; padding-left:11px; padding-right:11px; padding-top:10px; padding-bottom:0" valign="top" width="400"> <div style="border-style:solid; border-width:0px; padding-top: 0px; padding-bottom: 6px">  6. <a href="effects1.htm"> EFFECTS OF WAVEFRONT ABERRATIONS</a> 6.1. <a href="effects1.htm"> Aberrations and optical quality: Criteria</a>* 6.2. <a href="general_effects_of_aberrations.htm"> General effects</a>   6.3. <a href="aberrations_point.htm"> Object type related</a>* <a href="aberrations_extended.htm"> 2</a> 6.4. <a href="diffraction_pattern_and_aberrations.htm"> Diffraction pattern</a>    <a href="star_testing_telescope.htm"> Star test</a>* 6.5. <a href="Strehl.htm"> Strehl ratio</a>   6.6. <a href="mtf.htm">MTF</a>* <a href="mtf3.htm"> 2</a> <a href="mtf2.htm">3</a>  7. <a href="obstruction.htm"> OBSTRUCTION EFFECTS</a> <a href="central_obstruction_effect.htm"> 2</a> <a href="telescope_central_obstruction.htm"> 3</a> <a href="spider.htm">4</a>* <a href="apodizing_mask.htm"> 5</a>*  8. <a href="reflecting.htm"> REFLECTING OBJECTIVES</a> 8.1. <a href="reflecting.htm"> Newtonian</a>*   <a href="newtonian_off_axis_aberrations.htm"> off-axis</a>  <a href="newtonian_collimation.htm"> collimation</a>  <a href="newtonian.htm">diagonal flat</a> 8.2. <a href="two-mirror.htm"> All-reflecting two-mirror</a>* <a href="two_mirror_telescope_aberrations.htm"> 2</a>* <a href="classical_and_aplanatic.htm">3</a>* <a href="dall_kirkham_telescope.htm"> 4</a> <a href="loveday_two-mirror_telescope.htm"> 5</a><size="3">* <a href="two-mirror2.htm">6</a> 8.3. <a href="three-mirror.htm"> Three-mirror</a> <a href="three-mirror.htm">Cassegrain-Gregorian</a>   <a href="paul-baker_telescope.htm"> Paul-Baker</a>*    <a href="paul-baker_telescope.htm#The_FAA1">FAA</a> 8.4. <a href="tilted2.htm"> Off-axis and tilted elements</a> <a href="tilted2.htm">Herschelian</a>  <a href="tilted_component_telescopes.htm"> 2-mirror TCT</a>* <a href="TCT_2.htm">2</a>* <a href="tilted3.htm"> off-axis Newtonian</a>* 9. <a href="refractor.htm"> REFRACTING OBJECTIVE</a>* <a href="achromats.htm"> Achromat</a><size="3>*  <a href="apo_refractor.htm"> Apo</a> <a href="semiapo_and_apo_examples.htm">2</a>* <a href="designing_doublet_achromat.htm">Designing</a>    10. <a href="catadioptric.htm"> CATADIOPTRIC TELESCOPES</a> 10.1. <a href="catadioptric.htm#follow"> SUB-APERTURE LENS CAT</a><a href="catadioptric.htm#follow">s</a> <a href="sub_aperture_corrector.htm"> 2</a> <a href="field_flattener.htm">3</a> <a href="lens_corrector_examples.htm"> 4</a>* 10.2. <a href="catadioptric_telescopes.htm"> FULL-APERTURE LENS CATs</a> 10.2.1. <a href="catadioptric_telescopes.htm"> Dialytes</a>  <a href="catadioptric_telescopes.htm#telescope"> Hamilton</a>  <a href="schupmann_medial_telescope.htm"> Schupmann</a>  <a href="honders_camera.htm">Busack/Honders</a> 10.2.2. <a href="Schmidt-camera.htm#Schmidt_camera"> Schmidt corrector</a> <a href="Schmidt-camera.htm#Schmidt_camera"> Schmidt camera</a> <a href="schmidt_camera_aberrations.htm">2</a>*   <a href="Wright.htm"> Wright, Baker, Hyperstar</a>*  <a href="SN.htm">SN</a>   <a href="SCT.htm">SCT</a>* <a href="SCT_off_axis_aberrations.htm"> 2</a>* <a href="SCT2.htm">3</a>* <a href="schmidt_cassegrain_cameras.htm"> SC camera</a> 10.2.3. <a href="Mak-camera.htm"> Meniscus corrector</a> <a href="Mak-camera.htm">Bowers/Maksutov camera</a> <a href="maksutov_corrector_radii.htm"> 2</a>  <a href="Mak-Newton.htm">MN</a>* <a href="maksutov_cassegrain_telescope.htm"> MCT</a>* <a href="Mak_spherical.htm">2</a> <a href="MCT_off_axis.htm">3</a>* 10.2.4. <a href="Houghton.htm"> Houghton corrector</a> <a href="Houghton.htm#that_is_needed">Houghton camera</a> <a href="Houghton_camera.htm"> 2</a>  <a href="Houghton_telescope.htm">HN</a>  <a href="Houghton_telescope.htm#Chromatic"> HCT</a> <a href="Houghton_2glass.htm">2</a> <a href="HCT_plano.htm"> 3</a> <a href="HCT_design.htm">4</a> <a href="houghton-cassegrain_comparison.htm"> 5</a>  11. <a href="miscellaneous_optics.htm"> MISCELLANEOUS OPTICS</a>*  12. <a href="eyepiece1.htm"> TELESCOPE EYEPIECE</a>* <a href="eyepiece_aberrations_1.htm"> 2</a>* <a href="eyepiece_aberration_2.htm"> 3</a>* <a href="eyepiece_raytrace.htm"> 4</a>*  13. <a href="eye.htm"> THE TELESCOPIC EYE</a>* <a href="eye_aberrations.htm"> Aberrations</a> <a href="monochromatic_eye_aberrations.htm"> 2</a> <a href="2nd_order_eye_aberrations_off.htm"> 3</a> <a href="higher_order_eye_aberrations.htm"> 4</a> <a href="eye_chromatism.htm">5</a> <a href="combined_eye_aberrations.htm"> 6</a>* <a href="eye_intensity_response.htm"> Response</a> <a href="eye_spectral_response.htm">2</a>  14. <a href="early telescopes.htm">TELESCOPES</a> <a href="early telescopes.htm"> Past</a>* <a href="ATM_telescopes.htm">ATM</a>* <a href="OBSERVATORY_TELESCOPES.htm"> Observatory</a>* <a href="commercial_telescopes.htm">Commercial</a> *    APPENDIX: <a href="appendix.htm">Telescope specifications</a> <a href="appendix2.htm">2</a> <a href="appendix3.htm"> 3</a> <a href="appendix4.htm">4</a> </div> </td> </tr> <tr> <td align="center" colspan="2" height="155" style="text-indent: 21; padding-left:21px; padding-right:21px; padding-top:22px; padding-bottom:6px" valign="top">  *Last updated 2022   *2023    <size="3">*2024 <form action="http://www.google.com/search" method="GET"> <input name="ie" type="hidden" value="UTF-8" /> <input name="oe" type="hidden" value="UTF-8" /> <table> <tbody> <tr> <td> </td> <td style="padding-left: 12px"> <input maxlength="255" name="q" size="33" type="text" value="" /> <input name="btnG" type="submit" value="Google Search" /> <input name="domains" type="hidden" value="http://www.telescope-optics.net" /> <input name="sitesearch" type="radio" value="" /> www <input checked="checked" name="sitesearch" type="radio" value="http://www.telescope-optics.net" /> site </td> </tr> </tbody> </table> </form> Web-published on July 14. 2006. by <a href="mailto:webpub@fastmail.com"> Vladimir Sacek</a> </td> </tr> </tbody> </table> </div>  </body> </html