CLOCK
To evolve from apes 7 hrs
Homo Sapiens so far 10mins
Human history 30secs
1000 years 3secs
I year 3msec
HOW IT's DONE - ASTROPHOTOGRAPHY
Astrophotography
The range of astronomical objects is huge from; the bright Sun to distant galaxies, and from the Milky Way that surrounds the earth to individual stars. The first discoveries came from human viewing through simple telescopes that both magnified features and collected more light from dim objects. Analog photography allowed longer exposures to make even dimmer objects visible. Modern digital photography allows adding or “stacking” of images, along with remarkably low noise cooled cameras, mass produced optics and scanning stages, which has opened up astrophotography to amateurs.
MILKY WAY
Photographing the Milky Way requires largest possible field and f number. a 20mm focal length f2 full field lens allows a full sky mosaic with around 40 images 94 degrees per field. A 20 sec untracked exposure at 2000 ISO on a astro mod camera images stars down to magnitude 10, and many nebulae. A 8mm fisheye lens mirror compatible lens will allow filters with a 2.5 um pixel camera (QHY or ASI), will give 50-75 degree field of view and enchanced color contrast Milky Way.
Milky way with foreground looking away from moon. Full moon rises in east at dusk, sets in west at dawn. Waxing -increasing- moon sets in west around midnight. Waning - decreasing - moon rises in east at dawn.
NEBULA
The nebula within the Milky Way are some of the most visually interesting features with sizes from several degrees around Orion, to 10's of minutes. Nebula are the best candidates for HOS line filter images. Near the core visible in Summer, around Andromeda in Fall, Orion in Winter.
GALAXIES
There are a few large close galaxies such as Andromeda at 3 degrees, but the majority are smaller than the moon down to a few minutes of arc such as Whirlpool, and Leo Triplet. They tend to be visible in the Spring directly overhead in Virgo and Ursa Major.
PLANETS
The planets are much higher brightness and much smaller (20-40) arcsecs, so long focal lengths and large aperture for resolution are the key requirements. Seeing limits effective resolution, can be as low as 0.4 arcsecs. "Lucky imaging" is critical. Need at least 100 best images to stack.
Angular Nebulas Galaxies Planets
width deg
10 L. Magellenic
6 Rho Ophicho
3 N American Andromeda
2 Rosette/Lagoon
1 Orion / Elephants T Triangulum / Leo Trip/Bode
30' Flame/Eagle/Cats Paw & Eye Moon
15' Helix Whirlpool
6' Crab
1' Clown Faced
40" Jupiter
20" Saturn
10" Mars
Terrestrial astrophotography has 2 practical limitations, atmospheric seeing and light pollution.
A 1.0″ disk of seeing for a single star is a good one for average astronomical sites. The seeing of an urban environment is usually much worse. Good seeing nights tend to be clear, cold nights without wind gusts. Warm air rises (convection), degrading the seeing, as do wind and clouds. At the best high-altitude mountaintop observatories, the wind brings in stable air which has not previously been in contact with the ground, sometimes providing seeing as good as 0.4". Seeing disk 0.4 arcsecs in a hundredth of a sec. is regarded as "good" available at Mauna Kea.
Seeing for best Jupiter in Nikon P1000 is 1.6" (edge resolution 0.8") requires 4000f@25% to get decent image, and matches lens performance, should see some improvement with better seeing.
Seeing Rankings
1) < 0.4" Excellent
2) <2
3) >2
4) > 4 Poor
Atmospheric distortions or “seeing” limits the smallest angular feature to around 0.5-1 asecs, making planets such as Saturn at 20 asecs the smallest extended object that can be imaged. The effect of seeing on bright objects can be reduced by stacking multiple images - “Lucky imaging” where 1000’s of images are collected and the best 10-20% stacked.
Background light pollution is a problem everywhere except really remote high altitude locations. A very dark location such as Big Bend in Texas has a background that will allow galaxies 100 M light years away to be photographed by amateurs. Fortunately these are usually around 100’s asecs across and can be imaged in spite of terrestrial seeing. The huge professional terrestrial telescopes can collect light from much more distant objects that appear as point sources. The Hubble telescope in space has no atmospheric problems and can resolve 0.05 asecs.
The background light level is classified by Bortle level, and settles the maximum exposure time to achieve an IU value of around 50. The Bortle level roughly relates to relative brightness.
Each unit of magnitude roughly 2.5x in brightness. Each Bortle unit is worth roughly 1.25x in background brightness.
Bortle Visible Mag Camera Mag
Austin 5 6 9
Wimberley 4 6.5 9.75
Enchanted R 3 7 10.5 Good MW core
Junction 2-3 7.25 11 Good MW edge including Nebula
Big Bend 1 8 12.5
Lens selection.
A collection of lenses is need to cover the size range of objects of interest. The focal length of a lens defines the lens’s angular field of view. For a given sensor size, the longer the focal length produces a narrower angular field of the lens. Telescopes have focal lengths of 400mm or above, and can be made “diffraction limited” where the resolution only depends on the aperture of the objective. In addition, light collected is measured as the “f number” equal to the ratio of Focal Length to Aperture. The light transmitted scales as the area of the aperture or f number squared, so a f6 lens compared to a f2 lens transmits 3^2 = 9x less light. Wider angle lenses with focal lengths < 200mm have performance limited by aberration correction. Typically they can have resolution better than 1/1000th of the image angular field with a f number around 2.
Aberrations are quantified through Zernike Coefficients that measure geometric components of wavefront error. The wavefront errors reduce the intensity from diffraction limited spot quantified as the Strehl ratio. A Strehl ratio of 0.8 is regarded as "well corrected" and the FWHM increases as 1/Strehl ratio, or 1.6x theoretical limit. A 100mm lens has a 20degree field and a Strehl ratio of 0.1 equivalent to a resolution limit of 50 arcsecs.
Stopping down the aperture, to the point where the f# matches the resolution will minimize aberrations. A 400mm lens with a 6 degree field, gets close to a diffraction limited design. A small field for a small camera chip, such as the Nikon P1000 6mm phone chip, with a 1degree field is much easier to make diffraction limited.
Lens resolution can be measured as spot size FWHM or HSR, MTF of l/s = 0.5, or 2x edge width 75-25%.
The Milky Way covers the 180 degrees of the night sky, a “fish eye” lens with 8mm Focal Length (FL) can image the complete night sky in two images at right angles in a full frame 35mm SLR. Refractive lenses cover the range from 8-400mm FL with progressively smaller angular field down to 6 degrees and with proportionally better resolution.”
A 400mm refractive lens can be made “diffraction limited” so resolution in asecs is given by the “Rayliegh” or “Dawes” criteria as 115/aperture in mm for the distance between 2 distinguishable stars or "pitch". FHWM will equal half the Rayleigh resolution. The apertures size of a refractive lens is limited to <90mm by the cost and weight of the glass lens. The diffraction limited resolution of a typical 400mm FL 80mm aperture lens is 1.4 asecs with a f number around 6. The increase in f number is significant, as a result around 10x LESS light is collected compared to an f2 lens.
At 400mm FL, larger aperture reflective mirrors are more cost effective. There are three main cassegrain designs: Schmidt-Cassegrains, Maksutof-Cassegrains, or Schmidt Cameras. The Schmidt uses spherical mirrors, the Maksutof uses parabolic mirrors. There are numerous configurations to allow access to the focus of the lens, the most compact is the Schmidt Cassegrain (SCT) a catadioptric astrophotographic telescope designed to provide wide fields of view with limited aberrations. The design was invented by Bernhard Schmidt in 1930. In Cassegrain configuration, a curved secondary mirror increases the FL by 5x which moves the focus back through the main mirror. The cost of the mirrors is much lower if they are spherical. The Schmidt corrector plate is an aspheric refractive lens which corrects the spherical aberration in Schmidt–Cassegrain Telescope (SCT) designs. The primary mirror has a focal length of around 400mm. The SCT has a focal length around 2000mm with a f number around 10 and resolution <0.7asecs.
A Schmidt camera is the interesting modification for photography is to replace the secondary mirror that sits in a hole in the corrector plate, with a camera at the prime focus.
The refractive optics at the prime focus must correct for abberrations usually taken care of by the spherical secondary mirror, and depend on the acceptance angle of the optic. The lens resolution can be estimated from the Airy disk diameter of first null = 2.44*lambda * f#, 520nm f2 - Airy disk 2.5um.
In Celestron SCT the optics have evolved from Fastar, to Hyperstar, now there is a Celestron in house version "Rowe Ackerman". In Schmidt camera configuration, the lens becomes very fast f2 lens with a roughly 300mm FL .
https://sctscopes.net/SCT_Basics/SCT_OTAs/sct_otas.html
https://sctscopes.net/Photo_Basics/Fastar___ST-237/fastar___st-237.html
https://astronomynow.com/2016/06/01/celestron-rowe-ackermann-schmidt-astrograph//
Starizona sell “Hyperstar” correction optics that replace the secondary and produce 4asec resolution images. US7595942B2 LIGHT COLLIMATING SYSTEM FOR A SCHMIDT CASSEGRAN TELESCOPE Inventor Dean B. Koenig aka Starizona.
The resolution of the system is limited by the Hyperstar and is a function of f#. The HyperStar systems are not diffraction limited and are designed to produce a spot size roughly 2.5 times the size of the Airy disk, or a Strehl ratio of 0.45. The Airy disk of f2 300mm optic is 1.7 arcsecs. Therefore the design limit of Hyperstar is FWHM = 3.5 arc secs.
Lens Performance
Focal L Aperture f Resolution
20mm 50mm f2 200 arc secs
100mm 50mm f2 50 arc secs
300mm 150mm f2 4 arc secs
480mm 80mm f6 2 arc secs
1500mm 150mm f10 0.4 arc secs
Digital photography
First widely available commercial digital camera introduced in 1990 with a CCD camera. By early 2000's, CMOS cameras had taken over to the point where the film businesses were no longer viable. In the 2010's, the availability of affordable low noise CMOS cameras has revolutionized amateur astrophotography. Initially, this was achieved with large pixels such as the Sony 7a. Recently, cooled cameras with Exmor - R technology allow much longer exposures and narrow band filters.
To take advantage of the resolution of the lens, the pixel resolution must be matched to the lens resolution. Similar to the image angular field of view, the angular resolution of a camera pixel is measured by the pixel size divided by the lens focal length. Shannon's sampling theorem, which states that the digitizing device must utilize a sampling interval that is no greater than one-half the size of the smallest resolvable feature of the optical image. i.e. 2 pixels per line or 2x2 inside FWHM. In practice for planets, working at the resolution limit need to use the 5x optical multiplier to get full grey scale information.
The exposure time varies with the brightness of astronomical objects from the Sun to distant galaxies.
The relative brightness of an image as measured by the camera using f2 lens as a reference = 1/ aperture loss / exposure time / ISO
A typical exposure of the moon is 1/400 at ISO200 using a f6 lens that looses 10x light compared to f2. The relative intensity of the moon is 20 sec-1 ISO-1. The benchmark exposure for the Milky Way that shows details of nebula with a f2 lens is 20 sec at ISO 2000 = 2 E-5 sec-1 ISO-1. This is consistent with Magnitudes, the difference in intensity between the moon (M9) and nebula (M-5) is 5E-6. The practical limit on a single image exposure time is the background light level which can vary 6x depending on the Bortle level of the location, a practical target exposure level is around 50(8bit) levels.
Todays CMOS camera chips collect intensity with 12 bits of information equal to 4096 grey levels or 16x more than is usually displayed in a 8 bit image. When the image is stored as a RAW image, the intensity profile can be stretched and a 10x lower exposure can produce a good looking image.
To take advantage of the 12 bit dynamic range by stretching the intensity profile, the background noise must be very low, around 1 grey scale 8 bit level. The Sony Exmor Back Side Illuminated technology has a 6x lower noise than conventional camera chips. With cooling, a noise of 1 grey scale 8 bit level can be maintained for exposures of several minutes.
However, most CMOS imagers do have amplifier noise and hot pixels that still requires dark subtraction. After averaging multiple images, further reducing noise using Topaz AI noise reduction is an effective first step in image processing before stretching the intensity levels.
Commercial cameras from QHY and Svbony have 2um pixels and are available with and without cooling. The number of pixels or chip size determines the angular view of the image, and the cost of the camera. In 2022, a 4mm chip camera goes for $2-300, a 10mm chip for $6-900, a full frame 35mm chip for $2-3K.
Scanning stage
When exposure times get long, the earths rotation causes streaky star trails and the camera must be mounted on a scanning stage to offset earths rotation at 15 asecs/sec. The maximum exposure time without streaking is equal to the Pixel resolution divided by the Earths rotation rate.
For eyepiece viewing, a scanning stage with 1 horizontal (Azimuth) and 1 vertical rotation plane (Altitude) stage keeps the eye piece at a convenient position. For photography a “German Equatorial Mount GEM” is much more effective where 1 rotational axis (Right Ascension RA) is aligned to the earths rotation and the other is at right angles (Declination DEC). The motorized stages sit on a Alt/Az mount stage to align the RA to the earths axis. In principle, the earths rotation is offset by RA motion only.
I measured the performance of my Celestron AVX Gem stage. To achieve the very small stage moves, the motor is attached to a worm gear that cycles every 180 secs. When the RA axis is carefully aligned to the earth’s axis, the resulting errors produce a star with FWHM of 1.2 asecs for exposure times <30 sec, and 8 asecs for a 180 sec exposure. For very long exposures, misalign to the earths axis causes even larger errors that grow at 0.02 asecs/sec.
The simplest fix is to use a guide camera to provide feedback of any scan errors to the stage. Using a 400mm lens and camera with 4 asec resolution as guide, the resulting errors produced stars with FWHM 1.5 asecs for exposures of over 200 secs.
Spectrum filter
The light from astronomical objects has a number of characteristic emission lines from their components, a few in the visible can be used for terrestrial imaging; the H alpha line 656nm, Sulpur 672nm and Oxygen 496nm. These filters enhance color contrast, and have been popularized by the spectacular images from the Hubble telescope. The filters reduce the effect of light pollution by 2 magnitudes, at the cost of decreasing light intensity by 100x.
The "Hubble palette" uses SHO in wavelength order as the RGB channels which produces a green dominant due to the strength of H emission. This can be modified to a yellow/blue look. H and S are very similar in wavelength, and a popular alternative is HOS where G channel is the major variable which also gives a yellow/blue or yellow green look. My favorite is HOO or HSO, which gives a red/purple look which looks more realistic for a H emission nebula.
The filter holders are around 30 mm thick, so lenses require at least that distance from lens flange to camera flange ("back focus distance"). Telephoto lenses, 400mm refractor and 1500mm reflector in both SCT and RASA configurations typically have large back focus. The much lower light intensity with line filters make large f number optics a priority. The RASA configuration reflectors have f2 optics with 300-400 mm focal length. Short focal length large f number lenses (100mm and 8 mm) for mirror DSLR have 44mm back focus so that can be used for filters. There is a Canon EF mount to T2 adaptor that includes a filter drawer. Camera chips with 2um pixels are typically small so 1.25" filters can be used.
Optolong L-Ultimate 2" Filter. Use over a RGB camera to capture HOO image in one shot on a cooled
The L-Ultimate is similar to Optolong's L-eNhance and L-eXtreme filters in that it is a dual band filter that allows the transmission of Oxygen III and Hydrogen Alpha wavelengths, but the L-Ultimate only allows a 3nm bandwidth, compared to the 7nm of the L-Extreme!
Stacking
Image stacking is used for long exposures - longer than the atmospheric background limit, and/or tracking drift. Also used to align filter "RGB" or "HOS" images. Use RAW images, with "Drizzle" if pixel limited with less than 2 pixels for FHWM.
For bright object such as planets, use "Lucky Imaging" which is a stack where only the best 1-10% images are stacked, to minimize seeing. Can reduce FWHM by up to 3-4x. Need uncompressed, max bit depth, unpixellated images for best results. DO NOT use video which is automatically compressed.