The following is amateur work product. Criticism and corrections are appreciated. This opinions put forward here on recommended effective focal lengths to image the LCROSS impact differ slightly from the official Citizen Science LCROSS recommendations on the "About" page. See url: http://apps.nasa.gov/lcross/about/ This note is based on a discussion of Roger Sinnott's nomogram for choosing an effective focal length at url: http://media.skyandtelescope.com/images/Linked.gif Imagers can be best prepared to capture the impact by brainstorming and discussion of techniques before this unique one-shot impact event. I. Optimal resolution theory Modern imaging theory suggests that the optimal resolution images can be obtained by magnifying the full-width half-maximum (FWHM) size of the atmospheric seeing disk so that it subtends two pixel elements. Optimal resolution is achieved by matching the current seeing conditions to pixel element dimensions and to the target type. This guiding principle suggests focal lengths suitable for imaging the LCROSS impact depending on camera type, e.g. DSLR, CCD, high-end lunar planetary imagers (LPIs) or low-end LPIs. For discussion purposes, the LCROSS Team recommended 254mm (10 inch) aperture is assumed. For long-exposure amateur photography without the benefit with adaptive optics, the effective seeing disk size is equal to the current seeing conditions. If the seeing disk as disturbed by the atmosphere is 2 arcseconds that is the minimum resolution that can be achieved. This is because the exposure time for faint extended objects like nebulae are above 15 seconds. The disturbed atmosphere constraint controls, even where the theoretical resolving limit for a telescope (e.g. the Dawes limit) signficantly is less than disturbed seeing limit, i.e. 2 arcseconds. For long-exposure astrophotography, the imager seeks to take this 1, 2 or 3 arcsec disk and magnify it sufficiently to cover 2 pixel elements on their camera. For lunar and planetary imaging, the highest resolution exposure strategy is different because the objects are very bright. Exposure times can be corresponing low, for example around 0.036 second exposures (28 frames per second (fps) using a Meade DSI or 0.02 secs (60 fps) using an ImageSource mono camera). With the Meade DSI, I take very short exposures (0.01 seconds), but spaced at longer intervals. These low exposure times bring into play the possibility of the applying the poor man's adaptive optics - "lucky imaging". In lucky imaging, hundreds or thousands of exposures are gathered over an extended period in disturbed air. The hope is that luck will smile on the imager and that a few of those images will occur during subsec periods when the air is absolutely still. Lucky imaging brings into play the theoretical resolving power of the amateur's telescope. Recall that under optimal resolution theory, the full-width half-maximum (FWHM) size of the seeing disk covers two pixels. When lucky imaging is involved, that seeing disk is the theoretical resolving power of your telescope. The theorectical resolving power of a telescope can be related to the full-wdith half-maximum (FWHM) size of the telescope's Airy disk. The Airy disk is the diameter of the diffraction disk to the first diffraction dark ring and contains 84% of a point source's light energy. Dawes limit measures a radius, not a disk diameter. The Dawes limit is the radius of the diffraction disk to the first diffraction dark ring and contains 42% of a point source's light energy. The FWHM represents diameter of the Airy disk that contains 50% of the Airy disk's energy. For a 254mm (10") aperture, the Airy disk is 0.47", the Dawes limit is 0.46" and the FWHM is 0.40". to achieve optimal resolution, it is this FWHM diameter that the lunar planetary imager seeks to magnify across two physical pixel elements. A brief bit of math - the basic equation for finding the magnified size of an object on a flat plate at prime focus is: A_meters = lambda_radians * Fl_meter [Eq. 1] where: A_meters = the size of the object on the flat plate at prime focus in meters lambda_radians = the angular size of the object in radians Fl_meter = the focal length of the telescope Two assumptions are implicit in the the lucky imaging strategy for lunar and planetary imaging: 1) That are there brief subsecond moments when the image of the object is crisp. 2) That you can image sufficiently long enough that there is a good probability you will capture a sufficient number of these crisp images to be deconvolved into an even sharper imaging with image processing software. II. Pixel element sizes of modern LPIs, CCDs and DSLRs Modern LPI, CCD and DSLR cameras come in a wide variety of total chip size. The total chip size governs the total true field of few captured on the image and is not related to the size of the pixel elements on the chip. It is the size of the pixel elements that governs resolution. Modern LPI, CCD and DSLR chips can be divided roughly into classes by individual pixel element sizes in microns (um=microns), e.g. - ---------------------------------------------- Table 1: Physical pixel element sizes in microns Pixel Class | Type | Camera | Chip | Pixel size um | Pixel diag. um Small sq | High LPI | Imagesource DMK 31AU03 | ICX204AL | 4.6x4.6 | 4.6* Small sq | Mid rng LPI | ImageSource DMK 21AU04 | ICX098BL | 5.6x5.6 | 5.6* Small sq | Low end LPI | NexStar Celestron LPI | Unknwn | 5.6x5.6 | 5.6* Small sq | Low end LPI | Meade LPI imager | Unknwn | 6x6?? | 6* Small sq | High end LPI | Orion Starshoot | Aptina MT9V032 CMOS | 6x6 | 6* Small sq | Mid rng CCD | Orion Starshoot III | ICX285AL | 6.4x6.4 | 6.4* Small sq | DSLR | Canon ESO350D | Unkwn | 6.4x6.4um | 6.4* Small sq | Mid CCD | Meade DSI III | ICX285AL | 6.4x6.4 | 6.4* Mid range | High end CCD | Lumenera 2-1 | ICX205 | 7.6x6.2 | 9.8 Mid range | High end CCD | SBIG ST7 | Kodak KAF-400E | 9x9 | 9* Mid range | Old LPI | Quickcam LPI | Unkwn | 10x10 | 10* Mid range | Low end CCD | Meade DSI Pro I | Unknwn | 9.6x7.5 | 12.2 Large |High end CCD | Apogee AP8 | Kodak KAF-1000 | 14x14 | 14* Large | High end CCD | SBIG ST4 | Unkwn | 13.75x16 | 21 Large |High end CCD | Starlight | Sony ICX083AL | 23.2x22 | 22* * For square pixel elements, one side traditionally is taken as the controlling dimension. For rectangular pixel elements, the diagnol's length is used. ---------------------------------------------- III. Finding your effective focal length to match the optimal resolution for your camera with Sinnott's nomogram As a general rule-of-thumb for DSO imaging, the smaller the pixel element and the larger the seeing disk, a smaller focal length is applied to reach optimal resolution. Only larger pixel elements can match long focal lengths to a large seeing disk. This is why high end CCDs can have big pixel element sizes - they can stand high levels of magnification. This principle also explains what "binning" is about. Binning takes two small pixel elements and combines them into one pixel - effectively creating a larger pixel element that better matches higher magnifications. But in general, most amateurs are using cameras with smaller 12 micron and below pixel element sizes. The optimal resolution matching principle explains, in part, why SCT owners who want to use their 2000 to 3000mm focal length scopes to image DSOs first buy a focal reducer. Focal lengths under 2000mm best match long-exposure 1 and 2 arcsec seeing with the pixel element sizes of common CCDs and DSLRs. For lunar planetary imaging the rule-of-thumb is the opposite: a longer focal length is used with smaller pixel element sizes. Applying the theory of optimal resolution, for a Meade DSI Pro I with a 12.2 micron pixel (or 24.4 microns for two pixels), I would want to magnify the 0.40 arcsec FWHM disk (same as the 0.5 arcsec theoretical lucky image seeing disk) to about 22.4 microns. But based on experience, I'm going to use a 1 arcsec seeing disk with a FWHM of 0.6". Using the image scaling equation, I compute that I need about a focal length of 4700mm to achieve the optimal sampling resolution. Rather than deleve into imaging scaling math, a simple to apply nomogram that relates seeing disk size, the type of imaging (DSO or lunar planetary), chip size and effective focal length was published in S&T in 1997. Dennis di Cicco. _____. Of Pixel Size and Focal Reducers. Sky & Telescope. url: http://www.skyandtelescope.com/howto/astrophotography/3304356.html?showAll=y... (last Roger Sinnott's nomogram printed in the diCicco article is particularly helpful to understand these principles: http://media.skyandtelescope.com/images/Linked.gif Sinnott's nomogram is divided on the left side into imaging objectives - DSOs and Planetary-Lunar. Note the seeing disks for Planetary-Lunar are in the theoretical range of telescope performance above 10 inches of aperture, expressed in terms of the Airy disk size. The DSO left-hand scale is grouped around atmospheric constrained seeing at disk sizes of 1 or 2 arcsecs. On the right-hand side of Sinnott's nomogram is the pixel element size of a chip ranging from 30 microns down to an LPI's tiny 5 micron elements. See Table 1, above. For my Meade DSI Pro I example, drawing a line between 0.6 arcsecs on the left and a 12.2 micron chip element on the right, suggests a focal length of somewhere above 4000mm. For my 1200 mm focal length 10" aperture DOB, that translates into applying projection magnification of about 3.75x and 4x and an f-ratio of 4700mm/254mm or about f/18. IV. Applying optimal resolution and effective focal length to the LCROSS impact ejecta curtain. LCROSS is a hybird event that falls between a DSO imaging strategy and a lunar planetary lucky imaging strategy. On the one-hand, the impact is basically a lunar planetary imaging - invoking application of the lucky imaging strategy. On the other, the short-time frame and continuous change nature of the event - an ejecta that changes in size and brightness over a 60 second time frame - invalidates underlying assumption of the lunar lucky imaging strategy. Lunar lucky imaging assumes a stationary unchanging target over three or four minutes - sufficient to capture enough crisp images in still air that can be stacked and deconvolved using image processing software. Note Sinnott's nomogram with respect to the remaining discussion in this section: http://media.skyandtelescope.com/images/Linked.gif A) The LCROSS ejecta curtain and the lucky imaging strategy The conservative 95% probability simulation for the LCROSS ejecta curtain is an extended object about 10km by about 3km sticking up above a crater rim. This translates into an angular size of 5.6 arcsecs by 1.7 arcsecs. For a 10 inch (254mm) recommended aperature with an experience based resolution of 0.7 arcsecs FWHM and a 1.0 arcsec seeing disk, mentally, one would divide this linear object into 5 or 6 one arcsec "point" objects. To achieve optimal resolution, these five or six point objects get magnified so they subtend 10 or 12 pixel elements on your CCD chip or LPI of choice. If you are using a lunar planetary camera with 0.5 or 0.6 micron sized pixel elements, Sinnott's nomogram suggests using about a 2000mm efl. If you are using a CCD or DSLR camera with 12.2 micron sized pixel elements, Sinnott's nomogram suggests using about 4000mm of effective focal length. B) The LCROSS ejecta curtain and the traditional DSO strategy The conservative 95% probability simulation for the LCROSS ejecta curtain is an extended object about 10km by about 3km sticking up above a crater rim. This translates into an angular size of 5.6 arcsecs by 1.7 arcsecs. For a 10 inch (254mm) recommended aperature with seeing at 2.0 arcsecs with a 1.5 FWHM disk, mentally, one could divide the LCROSS linear ejecta curtain into 4 or 5 two arcsec "point" objects. To achieve optimal resolution, these four or five point objects get magnified so they subtend 8 or 10 pixel elements on your CCD chip or LPI of choice. If you are using a CCD or DSLR camera with 12.2 micron sized pixel elements, Sinnott's nomogram suggests using about 1500mm of effective focal length to acheive optimal resolution matching. C) The LCROSS ejecta curtain and a hybird strategy The hybird nature of the impact might justify a hybird strategy, e.g. - assume 1.5 arcsec seeing and 1.0 arcsec FWHM disk. For a 5 or 6 micron sized pixel elements of a planetary camera, Sinnott's nomogram suggests a very low 1000mm efl. For a larger 12.2 micron sized pixel elements of a DSO camera, Sinnott's nomogram suggests about 2000mm efl. This is the elf recommended on the LCROSS Citizen Science "About" page for DSLR cameras. V) Lunar glare and imaging the LCROSS ejecta curtain Large chip arrays in DSLRs and high-end CCD cameras may create a unique barrier. In a couple of prior notes, I mentioned articles by Bradley Schaefer on his modeling of lunar glare and its effect on the faintest magnitude star that can be seen during a lunar occultation. Post 8-29-2009 re: Schaefer's lunar glare effect on lunar occultation articles http://tinyurl.com/lkfv4c Post 8-30-2009 on S&T QBasic Program of Schaefer's lunar glare model http://tinyurl.com/mr2j2v Post 8-31-2009 Modified Schaefer occultation program http://tinyurl.com/kw6t88 The take-away point form playing around with Schaefer's lunar glare model, the faintest star visible - and thus the brightness of the sky just above the Moon - are significantly sensitive to the fraction of the Moon that is visible in your eyepiece. The larger fraction of the lunar disk that you have in your eyepiece or on your CCD chip, all the dark areas on your chip will read relatively brighter. Extrapolating this relationship to imaging the LCROSS impact, the lunar glare effect seems to weigh in favor of using higher magnifications and smaller chips that will capture a smaller fraction of the sunlit side of the Moon's terminator on CCDs chip. More glare will make the dark unlit portions of craters on the sunlit side of Moon (e.g. Caebus A and B) or the night sky above the dark limb of the lunar terminator relatively brighter and might reduce the contrast between the fainter ejecta curtain and its background. VI. More on differential photometry of dark crater areas Here's an image that I took this morning (9-8-2009) that is overexposed and at an elf of about 4000mm. Seeing was poor - the Moon was at a high altitude but the jet stream was right over my observing point and ran across the Moon's disk. The purpose of the image was to look at the differential photometry in the dark crater holes as compared to the night sky. In terms of ADUs from a raw image, the dark craters floor read about 0.4 mags brighter than the dark sky: http://members.csolutions.net/fisherka/astronote/observed/LCROSS/20090908_8U... http://tinyurl.com/n27edc VII. Conclusion Using an internet search, find the size of your camera's pixel elements. Use Sinnott's nomogram to estimate a recommended effective focal lenght for your telescope and camera. Then devise a projection magnification setup to magnify the 5 or 6 "points" that will match the LCROSS impact linear ejecta curtain object to the scale of your pixel camera estimates. Make a judgment call on which strategy you feel will be best - traditional DSO, lunar lucky imaging, or a hybrid between the two. See Sinnott's nomogram to choose a focal length that matches your strategy. Consider the effect of lunar glare on the TFOV covered by your image. Larger chips and lower magnifications will bring more of the Moon's brightly illuminated disk into the frame and increase the brightness of the background sky. Utlimately, there is no "right" answer and experienced imagers have to make a snap or gut judgment call on the best setup for there local seeing conditions. As always, this is guideline. Test and tweak for your particular gear. On the mornings of Sept. 9 and 10, the Moon will have an illuminated fraction similar to that which will be seen during the impact. It's a good time to test your setup. Considering seeing is a variable, you may want to test a long and short efl setup suitable for your camera's pixel element size. That way you can seemlessly pop in the right set up on impact day - the morning of Oct. 9. Clear Skies - Kurt References: Berry, R & Burnell, J. 2005. 2d. Handbook of Astronomical Processing. (HAIP). Willman-Bell. at page 8 Kitchin, C. 2003. 2ed. Telescopes and Techniques. Springer. ISBN 1-85233-725-7 at page 33 Schaefer, B. E. A star's visibility just before occultation. Sky Telesc., Vol. 85, No. 1, p. 89 - 91 (S&T Homepage) Bib. Code 1993S&T....85...89S