Making Your Own Astronomical Camera by Susan Kern and Don Mccarthy
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Noise and ISO CS 178, Spring 2014
Noise and ISO CS 178, Spring 2014 Marc Levoy Computer Science Department Stanford University Outline ✦ examples of camera sensor noise • don’t confuse it with JPEG compression artifacts ✦ probability, mean, variance, signal-to-noise ratio (SNR) ✦ laundry list of noise sources • photon shot noise, dark current, hot pixels, fixed pattern noise, read noise ✦ SNR (again), dynamic range (DR), bits per pixel ✦ ISO ✦ denoising • by aligning and averaging multiple shots • by image processing will be covered in a later lecture 2 © Marc Levoy Nokia N95 cell phone at dusk • 8×8 blocks are JPEG compression • unwanted sinusoidal patterns within each block are JPEG’s attempt to compress noisy pixels 3 © Marc Levoy Canon 5D II at dusk • ISO 6400 • f/4.0 • 1/13 sec • RAW w/o denoising 4 © Marc Levoy Canon 5D II at dusk • ISO 6400 • f/4.0 • 1/13 sec • RAW w/o denoising 5 © Marc Levoy Canon 5D II at dusk • ISO 6400 • f/4.0 • 1/13 sec 6 © Marc Levoy Photon shot noise ✦ the number of photons arriving during an exposure varies from exposure to exposure and from pixel to pixel, even if the scene is completely uniform ✦ this number is governed by the Poisson distribution 7 © Marc Levoy Poisson distribution ✦ expresses the probability that a certain number of events will occur during an interval of time ✦ applicable to events that occur • with a known average rate, and • independently of the time since the last event ✦ if on average λ events occur in an interval of time, the probability p that k events occur instead is λ ke−λ p(k;λ) = probability k! density function 8 © Marc Levoy Mean and variance ✦ the mean of a probability density function p(x) is µ = ∫ x p(x)dx ✦ the variance of a probability density function p(x) is σ 2 = ∫ (x − µ)2 p(x)dx ✦ the mean and variance of the Poisson distribution are µ = λ σ 2 = λ ✦ the standard deviation is σ = λ Deviation grows slower than the average. -
Chapter 3 (Aberrations)
Chapter 3 Aberrations 3.1 Introduction In Chap. 2 we discussed the image-forming characteristics of optical systems, but we limited our consideration to an infinitesimal thread- like region about the optical axis called the paraxial region. In this chapter we will consider, in general terms, the behavior of lenses with finite apertures and fields of view. It has been pointed out that well- corrected optical systems behave nearly according to the rules of paraxial imagery given in Chap. 2. This is another way of stating that a lens without aberrations forms an image of the size and in the loca- tion given by the equations for the paraxial or first-order region. We shall measure the aberrations by the amount by which rays miss the paraxial image point. It can be seen that aberrations may be determined by calculating the location of the paraxial image of an object point and then tracing a large number of rays (by the exact trigonometrical ray-tracing equa- tions of Chap. 10) to determine the amounts by which the rays depart from the paraxial image point. Stated this baldly, the mathematical determination of the aberrations of a lens which covered any reason- able field at a real aperture would seem a formidable task, involving an almost infinite amount of labor. However, by classifying the various types of image faults and by understanding the behavior of each type, the work of determining the aberrations of a lens system can be sim- plified greatly, since only a few rays need be traced to evaluate each aberration; thus the problem assumes more manageable proportions. -
High-Quality Computational Imaging Through Simple Lenses
High-Quality Computational Imaging Through Simple Lenses Felix Heide1, Mushfiqur Rouf1, Matthias B. Hullin1, Bjorn¨ Labitzke2, Wolfgang Heidrich1, Andreas Kolb2 1University of British Columbia, 2University of Siegen Fig. 1. Our system reliably estimates point spread functions of a given optical system, enabling the capture of high-quality imagery through poorly performing lenses. From left to right: Camera with our lens system containing only a single glass element (the plano-convex lens lying next to the camera in the left image), unprocessed input image, deblurred result. Modern imaging optics are highly complex systems consisting of up to two pound lens made from two glass types of different dispersion, i.e., dozen individual optical elements. This complexity is required in order to their refractive indices depend on the wavelength of light differ- compensate for the geometric and chromatic aberrations of a single lens, ently. The result is a lens that is (in the first order) compensated including geometric distortion, field curvature, wavelength-dependent blur, for chromatic aberration, but still suffers from the other artifacts and color fringing. mentioned above. In this paper, we propose a set of computational photography tech- Despite their better geometric imaging properties, modern lens niques that remove these artifacts, and thus allow for post-capture cor- designs are not without disadvantages, including a significant im- rection of images captured through uncompensated, simple optics which pact on the cost and weight of camera objectives, as well as in- are lighter and significantly less expensive. Specifically, we estimate per- creased lens flare. channel, spatially-varying point spread functions, and perform non-blind In this paper, we propose an alternative approach to high-quality deconvolution with a novel cross-channel term that is designed to specifi- photography: instead of ever more complex optics, we propose cally eliminate color fringing. -
Low-Cost Computational Astrophotography
Low-cost Computational Astrophotography Joseph Yen Peter Bryan Electrical Engineering Electrical Engineering Stanford University Stanford University [email protected] [email protected] Abstract 2. Related Work When taking photographs of the night sky, long ex- Currently, most astrophotographers compensate for posure times help photographers observe many stars, the rotation of the earth by physically moving the cam- but the rotation of the earth results in long star streak era along with the earth. However, some attempts arcs about the celestial pole. An algorithm for re- have been made to remove this requirement. To accu- moving these star streaks and substituting accurately rately localize stars in streaked images, one researcher placed point-like stars is designed and implemented. has re-mapped the star streak to polar coordinates, so Images containing star streaks are transformed into that all stars will have the same point-spread function. ones with un-streaked starry skies while retaining This technique was designed for locating specific stars color and brightness information. The procedure is for the purpose of identifying specific stars, but will shown to work consistently on a 35-image dataset. be applicable for our purposes when removing star streaks [4]. Other factors besides streaking can cause quality degradation in star images, and attempts have 1. Introduction been made to correct this. These have used such tech- niques as Richardson-Lucy deblurring [2] and maxi- Astrophotography is a widespread pastime in which mally sparse optimization [1]. DSLR cameras are used to take images of objects in space. Certain factors make this a very expen- sive hobby. -
DSLR Astrophotography They Say… Start with a Joke
DSLR Astrophotography They say… start with a joke. DLSR Wide-field Astrophotography The Advantages It’s Relatively Inexpensive All you need is a DLSR camera …and a tripod You Don’t Need This! Nikon v.s. Canon Most DSLR astrophotographers use Canon cameras. Canon releases the details of the camera’s software. This allows the development of third party software, designed specifically for astrophotography. Nikon does not create a truly raw image A simple median blurring filter is always applied... removing many stars, as they are seen as noise. This prohibits precise image calibration. Some Nikons allow the “Mode 3” work around. Using Nikon’s Mode 3 Simply start the bulb time exposure and terminate it by turning off the camera. The camera sees this as a low-power warning and immediately saves the image without running the median blurring filter Testing For Mode 3 Availability Take a one-minute dark exposure in Mode 1. This is a raw image with “no noise reduction” selected. Take a one-minute Mode 3 dark exposure. If Mode 3 is available, that exposure will have noticeably more hot pixels and noise. For Starters… Keep It Simple Set the focus to infinity... before it’s dark Mount the camera on a sturdy tripod Use a wide angle lens (18mm is nice) Set the lens to its lowest f-stop Use the RAW image format, at the highest ISO setting Shoot 20-30 second exposures Take about five dark exposures (more on this later) …and you can get an image like this! Nikon D40X 18mm @ f/4 ISO 1600 Mode 1 4 30-Sec exposures 4 30-Sec darks After taking several Milky Way shots it may be time to get more adventurous. -
Glossary of Lens Terms
GLOSSARY OF LENS TERMS The following three pages briefly define the optical terms used most frequently in the preceding Lens Theory Section, and throughout this catalog. These definitions are limited to the context in which the terms are used in this catalog. Aberration: A defect in the image forming capability of a Convex: A solid curved surface similar to the outside lens or optical system. surface of a sphere. Achromatic: Free of aberrations relating to color or Crown Glass: A type of optical glass with relatively low Lenses wavelength. refractive index and dispersion. Airy Pattern: The diffraction pattern formed by a perfect Diffraction: Deviation of the direction of propagation of a lens with a circular aperture, imaging a point source. The radiation, determined by the wave nature of radiation, and diameter of the pattern to the first minimum = 2.44 λ f/D occurring when the radiation passes the edge of an Where: obstacle. λ = Wavelength Diffraction Limited Lens: A lens with negligible residual f = Lens focal length aberrations. D = Aperture diameter Dispersion: (1) The variation in the refractive index of a This central part of the pattern is sometimes called the Airy medium as a function of wavelength. (2) The property of an Filters Disc. optical system which causes the separation of the Annulus: The figure bounded by and containing the area monochromatic components of radiation. between two concentric circles. Distortion: An off-axis lens aberration that changes the Aperture: An opening in an optical system that limits the geometric shape of the image due to a variation of focal amount of light passing through the system. -
A Guide to Smartphone Astrophotography National Aeronautics and Space Administration
National Aeronautics and Space Administration A Guide to Smartphone Astrophotography National Aeronautics and Space Administration A Guide to Smartphone Astrophotography A Guide to Smartphone Astrophotography Dr. Sten Odenwald NASA Space Science Education Consortium Goddard Space Flight Center Greenbelt, Maryland Cover designs and editing by Abbey Interrante Cover illustrations Front: Aurora (Elizabeth Macdonald), moon (Spencer Collins), star trails (Donald Noor), Orion nebula (Christian Harris), solar eclipse (Christopher Jones), Milky Way (Shun-Chia Yang), satellite streaks (Stanislav Kaniansky),sunspot (Michael Seeboerger-Weichselbaum),sun dogs (Billy Heather). Back: Milky Way (Gabriel Clark) Two front cover designs are provided with this book. To conserve toner, begin document printing with the second cover. This product is supported by NASA under cooperative agreement number NNH15ZDA004C. [1] Table of Contents Introduction.................................................................................................................................................... 5 How to use this book ..................................................................................................................................... 9 1.0 Light Pollution ....................................................................................................................................... 12 2.0 Cameras ................................................................................................................................................ -
Zemax, LLC Getting Started with Opticstudio 15
Zemax, LLC Getting Started With OpticStudio 15 May 2015 www.zemax.com [email protected] [email protected] Contents Contents 3 Getting Started With OpticStudio™ 7 Congratulations on your purchase of Zemax OpticStudio! ....................................... 7 Important notice ......................................................................................................................... 8 Installation .................................................................................................................................... 9 License Codes ........................................................................................................................... 10 Network Keys and Clients .................................................................................................... 11 Troubleshooting ...................................................................................................................... 11 Customizing Your Installation ............................................................................................ 12 Navigating the OpticStudio Interface 13 System Explorer ....................................................................................................................... 16 File Tab ........................................................................................................................................ 17 Setup Tab ................................................................................................................................... 18 Analyze -
Topic 3: Operation of Simple Lens
V N I E R U S E I T H Y Modern Optics T O H F G E R D I N B U Topic 3: Operation of Simple Lens Aim: Covers imaging of simple lens using Fresnel Diffraction, resolu- tion limits and basics of aberrations theory. Contents: 1. Phase and Pupil Functions of a lens 2. Image of Axial Point 3. Example of Round Lens 4. Diffraction limit of lens 5. Defocus 6. The Strehl Limit 7. Other Aberrations PTIC D O S G IE R L O P U P P A D E S C P I A S Properties of a Lens -1- Autumn Term R Y TM H ENT of P V N I E R U S E I T H Y Modern Optics T O H F G E R D I N B U Ray Model Simple Ray Optics gives f Image Object u v Imaging properties of 1 1 1 + = u v f The focal length is given by 1 1 1 = (n − 1) + f R1 R2 For Infinite object Phase Shift Ray Optics gives Delta Fn f Lens introduces a path length difference, or PHASE SHIFT. PTIC D O S G IE R L O P U P P A D E S C P I A S Properties of a Lens -2- Autumn Term R Y TM H ENT of P V N I E R U S E I T H Y Modern Optics T O H F G E R D I N B U Phase Function of a Lens δ1 δ2 h R2 R1 n P0 P ∆ 1 With NO lens, Phase Shift between , P0 ! P1 is 2p F = kD where k = l with lens in place, at distance h from optical, F = k0d1 + d2 +n(D − d1 − d2)1 Air Glass @ A which can be arranged to|giv{ze } | {z } F = knD − k(n − 1)(d1 + d2) where d1 and d2 depend on h, the ray height. -
The Rise and Fall of Astrophotography Dr
Page2 GRIFFITH OBSERVER August The Rise and Fall of Astrophotography Dr. Joseph S.Tenn Department of Physics and Astronomy Sonoma State University Rohnert Park, California HONORABLE MENTION HUGHES GRIFFITH OBSERVER CONTEST 1987 Dr. Joe Tenn’s carefully crafted articles seem to be able to win a prize in the annual Hughes Aircraft Company Science Writing Contest any time he chooses to enter, and his students have occasionally won prizes, too. This heartens our outlook on higher education in America and provides interesting and unusual material for readers of this magazine. His last article, “Simon Newcomb, a Famous and Forgotten American Astronomer," appeared in the November, 1987, issue of the Griffith Observer, almost two years ago. It was saddled with several errors imposed by the editor, not the author, and we hope this time we have given Dr. Tenn’s most recent contribution more reliable preparation for print. His attention this time is fixed on the development of astrophotography. Onthe occasion of the January, 1987, American the first serious uses of chemical emulsions for Astronomical Society meeting in Pasadena, professional research. Less than fifty years earlier visiting astronomers were invited to tour the the first crude experiments suggested the Palomar Observatory. The five-meter telescope, possibility that astronomical information might be towering five stories above us, looked as imposing recorded photographically. as ever, although it had been in operation nearly four decades and was no longer the world's DaQUe"'9°iYPe$ largest. Astronomers were involved with photography The real surprise, to this visitor at least, was from its beginning. It was the French astronomer that the telescope is no longer used for photo- Francois Arago who made the first public graphy. -
Astrophotography Tales of Trial & Error
Astrophotography Tales of Trial & Error Dave & Marie Allen AVAC 13th April 2001 Contents Photos Through Camera Lens magnification Increasing 1 Star trails 2 Piggy back Photos Through the Telescope 3 Prime focus 4 Photo through the eyepiece 5 Eyepiece projection Camera Basics When the photograph is being exposed, Light directed to viewfinder the light is directed onto the film. The viewfinder is completely black. Usual photographic rules apply: Less light ! Longer exposures Higher f number ! Longer exposures Light directed to film Star Motion Stars rise and set – just like the Sun in the daytime. The motion of the stars can cause problems for astrophotography Star Motion Stars rise and set – just like the Sun in the daytime. The motion of the stars can cause problems for astrophotography Star Motion Stars rise and set – just like the Sun in the daytime. The motion of the stars can cause problems for astrophotography Star Motion Stars rise and set – just like the Sun in the daytime. The motion of the stars can cause problems for astrophotography Star Motion Stars rise and set – just like the Sun in the daytime. The motion of the stars can cause problems for astrophotography Tracking the motion of the stars during the exposure is called “guiding”. Requires a polar aligned mount and periodic corrections to keep the subject stationary relative to the camera. Done using slow motion controls – or more often with dual axis correctors. Guiding Photography Technique Guiding Required? Star trails No Piggy back Yes Prime focus Yes Photo through the -
To Photographing the Planets, Stars, Nebulae, & Galaxies
Astrophotography Primer Your FREE Guide to photographing the planets, stars, nebulae, & galaxies. eeBook.inddBook.indd 1 33/30/11/30/11 33:01:01 PPMM Astrophotography Primer Akira Fujii Everyone loves to look at pictures of the universe beyond our planet — Astronomy Picture of the Day (apod.nasa.gov) is one of the most popular websites ever. And many people have probably wondered what it would take to capture photos like that with their own cameras. The good news is that astrophotography can be incredibly easy and inexpensive. Even point-and- shoot cameras and cell phones can capture breathtaking skyscapes, as long as you pick appropriate subjects. On the other hand, astrophotography can also be incredibly demanding. Close-ups of tiny, faint nebulae, and galaxies require expensive equipment and lots of time, patience, and skill. Between those extremes, there’s a huge amount that you can do with a digital SLR or a simple webcam. The key to astrophotography is to have realistic expectations, and to pick subjects that are appropriate to your equipment — and vice versa. To help you do that, we’ve collected four articles from the 2010 issue of SkyWatch, Sky & Telescope’s annual magazine. Every issue of SkyWatch includes a how-to guide to astrophotography and visual observing as well as a summary of the year’s best astronomical events. You can order the latest issue at SkyandTelescope.com/skywatch. In the last analysis, astrophotography is an art form. It requires the same skills as regular photography: visualization, planning, framing, experimentation, and a bit of luck.