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Formulas and Optical Design Data Appendix 1 Formulas and Optical Design Data Calculating Eyepiece Magni fi cation FL[telescope] Magnification = FL[eyepiece] Notes: FL[telescope] means the focal length of the telescope in millimeters; FL[eyepiece] means the focal length of the eyepiece in millimeters. Estimating Eyepiece AFOV (Accuracy Generally Within 10 % of Actual) AFOV≈× TFOV Magnification Notes: TFOV is true fi eld of view in degrees; Magni fi cation is the magni fi cation produced by the eyepiece in the telescope. W. Paolini, Choosing and Using Astronomical Eyepieces, The Patrick Moore 413 Practical Astronomy Series, DOI 10.1007/978-1-4614-7723-5, © Springer Science+Business Media New York 2013 414 Appendix 1 Estimating Eyepiece Field Stop (Accuracy Generally Within 10 % of Actual) FL[telescope]× TFOV Field Stop ≈ 57.3 Notes: The fi eld stop results are in millimeters; FL[telescope] means the focal length of the telescope in millimeters; TFOV is true fi eld of view in degrees; This method will only provide approximate results as it does not account for distortions present in the eyepiece, however it should be accurate within 10 % or less of the correct value. Calculating TFOV (in Degrees) Based on Manufacturer Provided Data AFOV TFOV ≈ Magnification Notes: AFOV is the apparent fi eld of view of the eyepiece in degrees; magni fi cation is the magni fi cation produced by the eyepiece in the telescope. AFOV TFOV ≈ (FL [telescope]÷ FL [eyepiece]) Notes: AFOV means the apparent fi eld of view of the eyepiece in degrees; FL[telescope] means the focal length of the telescope in millimeters; FL[eyepiece] means the focal length of the eyepiece in millimeters. This method is only approxi- mate, as any distortions in the eyepiece’s fi eld of view will make the results inac- curate by as much as 10 %. Calculating TFOV (in Degrees) Based on Drift Time Observations of a Star DT[sec] TFOV = 239 Notes: DT[sec] means Drift Time in seconds. This method is only accurate when the star is near the celestial equator. TFOV=××÷ABS( DT[sec] .0041781 COS( DEC[st ar] 57.3) ) Appendix 1 415 Notes: ABS means absolute value; DT[sec] means drift time across the entire fi eld of view in seconds; COS means cosine; DEC[star] means the declination of the star in degrees. This method is accurate for any star chosen to drift time since the declination of the star from the celestial equator is taken into account. Calculating TFOV (in Degrees) Based on Field Measures Eyepiece Field Stop Diameter TFOV=× 57.3 FL[telescope] Notes: Eyepiece fi eld stop diameter is in millimeters; FL[telescope] means the focal length of the telescope in millimeters; COS means cosine; DEC[star] means the declination of the star in degrees. (Tape Measure[observed]× 57.3) TFOV = Distance[telescope-to -tape measure] Notes: Tape Measure[observed] means the number of inches (or millimeters) of the tape measure that are observed through the eyepiece in the telescope; Distance[telescope-to-tape measure] means the distance in inches (or millimeters) from surface of the objective of the telescope to the wall where the tape measure is mounted. Calculating the Exit Pupil of the Eyepiece and Telescope Combination FL[eyepiece] Exit Pupil = FR[telescope] Notes: FL[eyepiece] means the focal length of the eyepiece in millimeters; FR[telescope] means the focal ratio of the telescope, which is the focal length of the telescope in millimeters divided by the aperture of the telescope in millimeters. APERTURE[telescope] Exit Pupil = Magnification Notes: APERTURE[telescope] means the diameter of the main objective of the telescope in millimeters; Magni fi cation is the magni fi cation produced by the eye- piece in the telescope, which is the focal length of the telescope divided by the focal length of the eyepiece. 416 Appendix 1 Calculating Measurement Accuracy (1Value++ Value 2 ValueN ) Results = N Notes: When taking fi eld measurements, the measurement should be repeated several times, then the average taken using the formula for averages above. Once the average measure is calculated, then the formula for Accuracy below can be used to express the accuracy of the average. ()MaximumValue− MinimumValue Accuracy =± 2 Calculating Brightness Change 1 Brightness = (Magnification2÷ Magnification1)2 Notes: Magni fi cation1 is the magni fi cation fi rst used to observe an object; Magni fi cation2 is the magni fi cation used to observe an object the second time. Estimating Eye Relief Based on Optical Design Eyepiece design Eye relief AFOV # Lens elements Abbe (Ortho) » 0.80 × Eyepiece focal length 45° 4 Brandon » 0.80 × Eyepiece focal length 50° 4 Er fl e » 0.60 × Eyepiece focal length 60–70° 5 Explore Scienti fi c 120° Fixed 13 mm 120° 12 Huygens » 0.10 × Eyepiece focal length 40° 2 Kaspereit » 0.30 × Eyepiece focal length 68° 6 Kellner » 0.45 × Eyepiece focal length 45° 3 Kepler » 0.90 × Eyepiece focal length 10° 1 König » 0.92 × Eyepiece focal length 55–65° 3–5 LE (Takahashi) » 0.73 × Eyepiece focal length 52° 5 Lippershey/Galilean – 10° 1 Meade 4000 SWA/UWA » 0.70 × Eyepiece focal length 65°/82° 6–8 (continued) Appendix 1 417 (continued) Eyepiece design Eye relief AFOV # Lens elements Monocentric » 0.80 × Eyepiece focal length 25–30° 3 Nikon NAV-SW/HW Fixed 16–19 mm 72°/102° 7–12 Pentax XL/XW Fixed 20 mm 65°/70° 7 Plössl/Symmetrical » 0.68 × Eyepiece focal length 50° 4 Ramsden » 0.00 × Eyepiece focal length 35° 2 RKE » 0.90 × Eyepiece focal length 45° 3 Takahashi-UW Fixed 12 mm 90° 8–10 Tele Vue Delos Fixed 20 mm 72° – Tele Vue Ethos Fixed 15 mm 100–113° » 7–9 Tele Vue Nagler » 0.6–1.4 × Eyepiece focal length 82° 6–7 Tele Vue Panoptic » 0.68 × Eyepiece focal length 68° 6 Tele Vue Wide Field – 65° 6 Williams Optics UWAN Fixed 12 mm 82° 7 Appendix 2 Eyepiece Performance Classes Although there are many brands and lines of eyepieces, many can be grouped into similar performing classes. As an example, although there are many brands of Plössl sold, they all perform relatively the same with the bigger distinction between most being their build quality and varying eye guard designs. Optically, however, with only a few exceptions most present the same AFOV of between 50° and 52° and all provide a similar level of off-axis correction. The following table provides the brands and lines of eyepieces presented in this book, grouped into similar performing classes where their AFOVs and off-axis cor- rections are considered by other amateur astronomers to be very similar. When an observer is making a decision on choosing any eyepiece, researching the other eyepieces in these similar performance class listings will greatly assist the observer in making the best considered decision. Performance class Eyepieces 20° Couture Ball Singlet, Siebert Planesphere 30° Siebert Optics MonoCentricID 40° Antares Ortho, Apogee Super Abbe Orthoscopic, Baader Planetarium Classic Ortho, Baader Planetarium Genuine Abbe Ortho, Cave Orthostar Orthoscopic, Celestron Ortho, Edmund Scienti fi c Ortho, Kokusai Kohki Abbe Ortho, Kson Super Ortho, Masuyama Orthoscopic, Meade Research Grade Ortho, Meade Series II Orthoscopic, Nikon Ortho, Siebert Optics Star Splitter/Super Star Splitter, Takahashi Ortho, Telescope Service Ortho, Unitron Ortho, University Optics Abbe HD Orthoscopic, University Optics Abbe Volcano Orthoscopic, University Optics O.P.S. Orthoscopic Planetary Series, University Optics Super Abbe Orthoscopic, VERNONscope Brandon (continued) W. Paolini, Choosing and Using Astronomical Eyepieces, The Patrick Moore 419 Practical Astronomy Series, DOI 10.1007/978-1-4614-7723-5, © Springer Science+Business Media New York 2013 420 Appendix 2 Performance class Eyepieces 40° Astro-Physics Super Planetary AP-SPL, Pentax XO, Pentax XP, TMB Aspheric Ortho, TMB Supermonocentric, Zeiss CZJ Ortho, Zeiss ZAO I/ZAO II 40° Garrett Optical Orthoscopic 40° Meade Series II Modi fi ed Achromatic MA 40–65° Galland/Gailand/Galoc Ortho/Er fl e/König 45–55° Sky-Watcher LET/Long Eye Relief (LER) 50–52° Antares Plössl, Astro-Professional Plössl, Astro-Tech High Grade Plössl, Astro-Tech Value Line Plössl, Bresser 52° Super Plössl, Carton Plössl, Celestron Omni, Celestron Silvertop Plössl, Clavé Plössl, Coronado CeMax, Edmund Scienti fi c Plössl, Garrett Optical Plössl, GSO Plössl, GTO Plössl, Long Perng Plössl, Meade Series 3000 Plössl, Meade Series 4000 Super Plössl, Olivon Plössl, Opt Plössl, Orion HighLight Plössl, Orion Sirius Plössl, Owl Black Night Plössl, Parks Silver Series, Sky-Watcher SP-Series Super Plössl, Smart Astronomy Sterling Plössl, TAL – Symmetrical Super Plössl, Telescope Service Plössl, Telescope Service Super Plössl, Tele Vue Plössl, Vixen NPL 50–55° Celestron E-Lux (2″ models only), Celestron Kellner, Criterion Kellner, Edmund Scienti fi c RKE, GSO Kellner, Kokusai Kohki Kellner, Orion DeepView, Orion E-Series, Russell Optics (2″ 52 and 60 mm only), Sky- Watcher Kellner, Sky-Watcher Super MA Series, Telescope Service RK, Unitron Kellner 50–55° Celestron Er fl e, Kokusai Kohki Er fl e, University Optics Super Er fl e 50–60° Orion Optiluxe 50–65° GTO Wide Field 50–70° Russell Optics 1.25″/2″ Series 52° Antares Elite Plössl, Baader Eudiascopic, Bresser 60° Plössl, Celestron Ultima, Kasai Astroplan, Meade Series 4000 Super Plössl (pre-1994, smooth sided, 5-elements), Meade Series 5000 Super Plössl, Orion Ultrascopic, Parks Gold Series Plössl, Takahashi LE 55° Agena ED, Celestron X-Cel, Orion Epic ED II (older version), Vixen Lanthanum (LV), Vixen NLV 55° Astro-Professional Long Eye Relief Planetary, Astro-Tech Long Eye Relief, Long Perng Long Eye Relief, Orion Edge-On Planetary, Smart Astronomy SA Solar System Long Eye Relief, Stellarvue Planetary, William Optics SPL, Zhumell Z Series 55° Astro-Tech Long Eye Relief, Astro-Professional Long Eye Relief Planetary, Long Perng Long Eye Relief, Orion Edge-On Planetary, Smart Astronomy SA Solar System Long Eye Relief, Stellarvue Planetary, William Optics SPL, Zhumell Z Series 55° I.R.
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