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Astrophotography

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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.

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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. 

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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.

 

Exposure 20s ISO 200 f2  in Sony a7s camera gives good images, requires Bortle 2 or better.  

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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. 

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Exposure 15s ISO 3200 f6 for Lagoon, 2x needed for Eagle .  f2.8 gives overexposure, can live with Bortle 4.

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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. 

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Exposure multiple  30-60s  f2 gives good images.  1 hr and greater exposure show detail. 

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ARP 273 -300 Mlyr away, 2amin across, Mag13, C8 SCT 100x 5min (10hr) @ 10dB gain. 0.6 asecs /pix, 2 asecs spot size. With C6 RASA 4 asec resolution,  30min exposure G10. 

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Markarians chain 106 galaxies imageable with SCT-RASA 2 hrs exposure.

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The Hubble Deep Field (HDF) is an image of a small region in the constellation Ursa Major, constructed from a series of observations by the Hubble Space Telescope. It covers an area about 2.6 arcminutes on a side. 40 hours exposure at each of 4 wavelengths. 

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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. 

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Very bright so ISO 200, 1/1000s f6 is fine. 

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Angular                      Nebulas                          Galaxies                                      Planets             

width deg

10                                                                             L. Magellenic

6                             Rho Ophicho M7.5

3                                       N American                     Andromeda

2                      Rosette M5.5/Lagoon M46

1                      Orion M4 / Elephants T            Triangulum / Leo Trip/Bode

30'                       Flame/Eagle M6.4 /Cats Paw & Eye                                           Moon

15'                                  Helix                                  Whirlpool

6'                                     Crab                                  Stephan's Quintet

2'                                                                                ARP273

1'                                     Clown Faced

40"                                                                                                                                Jupiter

20"                                                                                                                                Saturn

10"                                                                                                                                Mars 

3"                                                                                                                                  Jupiter red spot

1.5"                                                                                                                               Ganymede

0.75"                                                                                                                             Europa

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1. Carina Nebula (Mag -1)

2. North America Nebula (Mag -4)

3. Orion Nebula (Mag -4)

4. Running Chicken Nebula (Mag -4.5)

5. Barnard’s Loop (Mag -5)  - around Orion

6. Lagoon Nebula (Mag -6)

7. California Nebula (Mag -6)

8. Flaming Star Nebula (Mag -6)

9. Eagle Nebula (Mag -6)

10. Omega Nebula (Mag -6)

11. Homunculus Nebula (Mag -6.2)

12. Trifid Nebula (Mag -6.3)

13. Soul Nebula (Mag -6). 

14.  Rosette Nebula (Mag -9.0)

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https://en.wikipedia.org/wiki/List_of_planetary_nebulae

https://astrobackyard.com/brightest-nebulae-in-the-sky/

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Galaxies

Galaxies scale are around 200 Mly across.   

1) Megallenic Clouds

2) M31 Andromeda  10x diameter away  Mag 3.5

3) Triangulum

4) Whirlpool - Ursa Major  & Pinwheel 100x diameter away  Mag -8 

5) Sombrero - Virgo

6) Needle 

7) Bode - Ursa Major

8) Leo Triplet - Leo

9) Markarian - Leo 

10) Perseus Cluster _ Perseus

11) Stephans Quintet - Pegasus near Andromeda  1000x diameter away.  Mag -16

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Terrestrial astrophotography has 2 practical limitations, atmospheric seeing and light pollution.

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The earth axis of rotation points at Polaris, so the sky appears to rotate about Polaris. In the plane of the Milky Way, Polaris is in the same direction as Andromeda, on the opposite side (North) of the Milky Way. The direction is directly away from the core of the Milky Way. 

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Stargazers are in for a treat on Saturday night as the Perseid meteor shower lights up the sky. The phenomenon brings up to dozens of meteors an hour, created when debris from comet 109P/Swift-Tuttle collides with the Earth's atmosphere and burns up. This year the event is peaking during the night of 12 August, into the early hours of 13 August.

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SUN 

The Sun is a black body emitter peaking at 500nm, and is white over the visible range. The elements in the sun appear as broad  absorption lines. The Ha line has a base width of around 10nm, width at half height 1.5nm. Therefore H rich areas appear dark relative to black body radiation, or blue in a RGB image.  In an 7nm bandwidth HSO image, the S & O wavelengths are filled by blackbody emissions.  At Ha, the texture in the sun are caused by variations in gas density  blackbody emissions AND  H content.  A narrower Ha filter matched to the emission line will help to reduce black body emissions and make the Ha re-emissions more visible. The narrow emission line is produced by a transition from the lowest excited state down to ground. The broad absorption line is created by continuous blackbody radiation exciting transitions into any matching excited states.

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If the filter  bandwidth is reduced to below  0.1nm, then the re-emission Ha  line is observed, and both prominences and disk emissions will have similar intensity. The narrower the filter width <0.03nm, the better the contrast of the emission line against the absorption of the black body radiation. Broader filters around 0.1nm are sufficient for the stand alone emission from prominences.

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For imaging absorption using interference filters >3nm bandwidth the choices are:

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Ca                                 394nm 7nm FWHM filter  5nm 1/2width    

OIII & Sun blackbody 501nm                                 7nm 1/2width

Ha                                 656nm 1.5nm FWHM         3.5nm 1/2 width

SII & Sun blackbody   672nm 

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https://bass2000.obspm.fr/solar_spect.php

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Try HOCa for 3 color image. CaOH will have hydrogen areas in red, Ca areas in blue. 

Solar filter should be rated ND 5.0, meaning they block 99.999 percent of the Sun’s light. Ha emissions are 0.001% or 1E5x lower in intensity than solar black body. 

https://general-tools.cosmos.esa.int/vex/sun_monitor.html

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If prominences can be seen with a >3nm filter, these hydrogen emissions that appear red in a RGB image and are therefore the compliment of the H absorptions in the surface of the sun. Eclipse blocks 1E3 of atmospheric scattering making the prominences visible. Without an eclipse, a high altitude clear sky would be essential. Try in Colorado ! 

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Seeing

Thermal turbulence causes image perturbations on the order of 10–5 to 10–4 radians (2 to 20 arcseconds).

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. 

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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. 

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The seeing using a scale ranging from 1 to 5. Categories Seeing in arc-second, To do this, astronomers aim at a star near the zenith of magnitude 2 to 3 and then visualize the diffraction pattern of the star. Finally, they estimate the seeing using a scale ranging from 1 to 5”.

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I>   4"            Boiling of the image tending towards the planetary aspect

II~  3.0-4."    Significant central disc eddies; evanescent or absent rings

III~ 1.0-2.0"  Deformations of the central disc; interrupted rings

IV~ 0.4-0.9"  Slight undulations running through the diffraction rings

V < 0.4"         Perfect and motionless image

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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.

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Seeing forecast ​

• High jet stream speeds (>20m/s) usually correspond to bad seeing.

• Bad layers have a temperature gradient of more than 0.5K/100m.  

https://www.meteoblue.com/en/weather/outdoorsports/seeing/austin_united-states_4671654

The model is phenomenological  as opposed to physical. The seeing values are computed based on the integration of turbulent layers in the atmosphere, the turbulence is estimated based on correlation with physical measurements of layers in the atmosphere. Balloons were launched at various locations with simultaneous seeing measurements.  Model accuracy predicting seeing  estimated as +- 40%.

https://iopscience.iop.org/article/10.1086/503165/pdf   - paper describing the APX model.

Publications of the Astronomical Society of the Pacific, 118: 756–764, 2006 May
A Model to Forecast Seeing and Estimate C2 Profiles from Meteorological Data, N.Herve Trinquet and Jean Vernin

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Background light 

A clear full moon as a light source will be fine for video on Sony7as f2.8.  Scene brightness is measured in lux. An f2.8 lens, 1/30s exposure, ISO12800 = 0.2 lux.  At  5E-3 lux  usable video at ISO409K, IR filter has no effect.   Shaded tree no moon has 2E-4 lux S/N=1 @ ISO409K, cooled camera QHY183   S/N 10x better and quality images at 1s G30 (ISO32k).  

https://toolstud.io/photo/light.php 

For moon light 100mm lens is fine, 400mm f8 would require 10x higher ISO and should be just usable. 

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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.

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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. ​

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Each unit of magnitude roughly 2.5x in brightness.  Each Bortle unit is worth roughly 1.25x in background brightness.  In junction TX, background was 33IU out 255 exposure  20s f2 ISO2000 = 2E-4 lux for Bortle 2.5. 

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                         Bortle       Visible Mag     Camera Mag     Background Lux 

Austin                5                  6                      9                      2E-3

Wimberley        4                  6.5                   9.75                 7E-4

Enchanted R     3                  7                     10.5                  3E-4 Good MW core

Junction             2-3               7.25                11                    2E-4 Good MW edge including Nebula 

Big Bend            1                  8                     12.5                 7E-5

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Lens selection. 

The amount of light captured by an optical system is proportional to the area of the entrance pupil that is the object space-side image of the aperture of the system. At a given focal length, a larger lens aperture equals a small f number and more light per pixel. An increasing focal length has a smaller field, larger f number and less light per pixel. Larger aperture lenses tend to have proportionally longer focal lengths to keep aberrations manageable.

 

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. Wider angle lenses with focal lengths < 200mm  have performance limited by aberration correction. Typically they can have resolution around 0.5ppm of the image angular field with a  f number around 2. Represents 15 um resolution at the image plane with 0.5 um wavelength light. 

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Using an artificial star 0.8 asecs in diameter and a large uniform pad as a references, I compared a C6 f2 RASA, 100mm fl f2 refractor, and a 400mm fl f6.3-16 refractor. A f2 comparing the C6 RASA and 100mm fl refractor he brightness of the star scaled with the area of the aperture. Overall image brightness goes down with increasing f number. For imaging collections of point sources such as galaxies, f2 vs f6 is 10x = 3 x in aperture diameter. A C6 RASA  and C14 SCT are roughly equivalent in galaxy imaging, with the SCT having better resolution.

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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. 

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Test target 2x2 pixel spots in a 2900 pixel image. When displayed on a lap top it produces 0.2 mm spots.    https://www.lonelyspeck.com/a-practical-guide-to-lens-aberrations-and-the-lonely-speck-aberration-test/

 "for a 4000 pixel image, an aberration level of 0.4% of pixel count or less is considered “excellent,” less than 1% is “acceptable,” while aberration levels of 1% or higher is considered “poor” performance." 0.4% corresponding to 20 pixels. Using the artificial star.....

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Lens resolution can be measured as spot size FWHM or Half Spot Diameter, MTF of l/s = 0.5, or 2x edge width 75-25%. Line width equal to FWHM equivalent to  MTF0.4 or 2x Rayliegh limit  (MTF0.1)

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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.” The change in field angle with focal length for a 35mm full frame is shown in the figure. 

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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". 

An MTF of 9% is implied in the definition of the Rayleigh diffraction limit, Roughly 1/2 linewidth at MTF = 0.5 

http://www.normankoren.com/Tutorials/MTF.html

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So for a 80mm optic such as 480R or Nikon P1000 MTF = 0.5 at 2.8 asecs. For the Seestar S50 Rayleigh resolution = 2.3 asecs or 4.6 asecs @ MTF0.5, should be matched by RASA SCT.

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MTF = 0.5 is 2 x Rayliegh resolution. There are some allowed abberations  to be "diffraction limited", the actual  resolution needs to be better than 1.6X Rayliegh resolution.

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The field size is reduced for non-full frame cameras by the chip diagonal. The pixel resolution is given by dividing the field size by the pixel count and any field reducer optics. 

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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.

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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). 

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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. 

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The central aperture "obscuration" reduces the MTF of the lens. A 30% obscure area reduces the MTF = 0.5 resolution by 2x, while the MTF = 0.25 remains the same. A 150mm SCT (C6) will resolve large features the same as a 75mm refractor. However the SCT will resolve 2x smaller features at low MTF, that may be contrast enhanced. 

https://www.beckoptronic.com/uploads/cms/productsdownload/14/beck-tn-performance-of-optics-with-central-obscuration-v2-file.pdf

 

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.

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Ritchey-Chrétien astrograph is an SCT configuration that uses hyperbolic mirrors to avoid a corrector plate and allows much larger apertures. A RC 14" at altitude has 0.4 asecs/pix and resolution 1.3 asecs produces excellent SHO Pillars image that with Topaz sharpening can get close to Hubble, 0.3 asecs/pix and 0.6 asecs spot with significant shoulder abberations. 

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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. 

https://www.edmundoptics.com/knowledge-center/application-notes/imaging/limitations-on-resolution-and-contrast-the-airy-disk/

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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//

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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.

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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. 

https://www.cloudynights.com/articles/cat/articles/the-amazing-hyperstar-a-guide-to-optimize-perf-r3013

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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           0.7 arc secs

4000mm    350mm       f10          0.3 arc secs

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Human factors 

The maximum angular resolution of the human eye is 28 arc seconds. Viewing a image filling 40 degree FOV (85"display at 10 feet) requires 5000 pixels on a side. 

Reading distance 15", page size 10" requires  500 dpi.  

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Reference measurements of eye resolution are;

423 ppi Young Human Eyes

340 ppi Above Average Human Eyes

300 ppi Average Human Eyes

254 ppi Most Human Eyes

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The candela per square meter (symbol: cd/m2) is the unit of luminance in the International System of Units (SI). TV typically around 100 cd m-2,  humans detect a 2% change in Luminance or 2(8bit)IU in an image centered on 125IU image. p569

Just Noticeable Color Differences 0.02 in 0.4 or 5%. 5(8bit)IU on 125IU image.  p576

RGB is 3 components so 3% per component RMS. 

Color Science: 2nd Ed  Wyszecki and Stiles.

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Conclusion: target noise should be < 2% on each channel, 300 dpi for close viewing print. 5000 pixels for large display. 

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Analog photography

Analog film had a specified sensitivity or film speed "ISO", a standard illumination level. Low (slow) ISO film has small silver crystals for bright and/or stationary objects and high resolution images. High ISO (fast) film had large crystals for dim subjects or fast moving subjects requiring short exposure times, with a loss of image resolution. For a given film, the photographer could play off exposure time against aperture or depth of focus.

For exposures greater than 1 sec, film looses sensitivity known as "reciprocity failure" which limits film for very long exposures of dim astronomical objects. 

 

High resolution film was bench marked at ISO100, high speed such as Tri-X is ISO400.  

0.05-2um silver halide crystal size. Dye cloud 1-10um. 

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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 allow much longer exposures and narrow band filters.

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Digital cameras are a perfect fit for creating digital images for digital media. Full frame digital cameras with 5um pixels run at low ISO get close to analog. The great advantage of digital is in programmable light sensitivity which can be combined with image processing for  noise reduction. Digital cameras make image stacking simple, which enables very long effective exposure times for very dim astronomical objects.

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In a digital camera  the spatial resolution of the camera is determined by the size of each pixel. 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. In a color camera, pixels are grouped in fours Red, Blue and two Green. During image processing, the R,G, and B values for each pixel are extrapolated from the 4 nearest neighbors of the same color  - "DeBayering". This does produce a slight loss of resolution so that the "effective" pixel size is around 1.3x actual pixel. Also, RBG cameras also have 4x lower ISO than the monochrome version, at the same gain level. The image must be stored as RAW to avoid any compression.

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Digital cameras use a very efficient (>85%) photodiode to convert the incoming photons to electrons that are stored in a capacitor or "well". To collect the image, each well is emptied and the electrons amplified, followed by Analog to Digital Conversion (ADC).  The image display standard is 8 bits or 256 grey levels. The amplifier gain in consumer cameras is specified as the "ISO" or effective film speed.

 

At a given light level, f number  and exposure time, the number of electrons in the well is determined by the area of each pixel, confirmed by the QHY cooled cameras all using backside illuminated Exmor R . The maximum number of electrons in a full well is a camera design parameter. At the base or lowest ISO illumination and exposure time, zero gain coverts a full well to a 255(8bit) IU pixel in the image typically under ISO50 conditions. With increasing amplifier gain the ISO increases and the full well size  (number of electrons) goes down.  A typical full well is 30,000 electrons in a 5um front illuminated pixel. To just generate 256 gray levels, the number of electrons must be at least 256 created by 100x less light, which corresponds to ISO5,000. The highest speed is obtained at 16 grey levels (photons) per pixel or ISO80,000. These are much higher ISO values compared to analog film. 

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The number of electrons (photons) in a pixel depends on the exposure time  and the light intensity, the number to fill the well depends on ISO. Shot noise, the random variation produced by a limited number of events, has a standard deviation of the square root of the number of electrons. A full well of 256 electrons has a shot noise of 16 electrons or 16 8bit grey scales. The graph of noise at different intensity levels within the image shows the Sony a7s  has a noise level of 15 grey scales at ISO16,000. This benchmarks the maximum ISO for a quality image. 

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Shot noise is the digital equivalent to grain size in analog. Image processing using AI tools such as Topaz on RAW uncompressed images, is very effective at reducing noise in images.  Apply noise reduction after color  balance is established. Use Topaz "sever Noise 25" settings. Noise reduction of 5x should be achieved, as shown.  In comparison, JPEG compression reduces noise at the expense of a lot of image detail, particularly in the color details. 

The shot noise cannot be avoided, the read out noise and dark noise needs to be minimal in comparison.  The large pixel in the Sony a7s allows a better quality read out transistor and A/D converter producing very low read and dark noise in comparison to Nikon P1000 and QHY83. Cooling the QHY 183 produces even lower dark noise than the Sony.   For really dim objects large collection angle (low f number) optics, very long exposures and/or multiple frames are needed to get capture enough photons. 

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Camera chip design can significantly increase amount of light captured at each pixel. The log log  graph of ave noise at different ISO shows  noise scaling with the square root of ISO.  The capture efficiency depends on the pixel size and fabrication technology. Sony  Exmor (Sony a7s) uses microlens on a front illuminated diode to focus light across the pixel into the diode region.  Sony Exmor-R developed in 2008 (Nikon P100) uses backside illumination of the diode, so that wiring does not block light - a 4.6x improvement for a small pixel 2um pixel. Exmor RS developed in 2021 (Iphine14) has the transistor is a separate layer underneath the diode increasing the diode area. The result is achieves a higher sensitivity of 2.5x and a lower random noise of -25% at a given pixel size.   ​

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Digital cameras can be characterized by performance at a reference condition, in this case pixel count and size, and performance at a constant number of photons in the photocell. The metrics are photospeed ISO  that just supports 256 grey scales as measured as ISO that produces shot noise std dev of 12IU for region of 125IU (bright indoor lighting best), dark image  read noise at 1/1000 s and dark noise in IU s-1 at 256 electrons in full well.  Figure of merit for light collection is photospeed ISO/pixel area. 

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Measurements show a 10x range in sensitivity at constant shot noise between different cameras. 

Sony a7s Exmor 12Mpix has a  large 8um square pixel f2.0.  It has 10x higher photo-speed at the same shot noise, compared to the Nikon P1000 f3.5, and a ISO max of 409k.  At ISO400 it has 2(8bit)IU noise, at reference Milky Way ISO2000 there is 4(8bit)IU noise. A 8 bit grey scale image is obtained with an ISO16,000. The advantage of back side illumination is much less for a big pixel. 

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Sony a9 III has Exmor RS 25Mpix  (6kx4k) resolution - 5um pixel with max ISO 51K, which seems moderate. Price $6K which is not. Shot noise  of S/N 4.1/181 @ISO1250 is very close to Sony a7S with 2.5x larger pixel. 

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Nikon P1000 Exmor R  16Mpix has a 1.55 um square pixel with the benefit of better electron from back side illumination 4.6x improvement . At the zero gain of  ISO100 it has 3(8bit)IU shot noise, an 8 bit grey scale image is obtained with an ISO1,600. The next step up will be an upgrade to a Exmor RS chip with 2x larger full well. 

 

The practical QHY183C Exmor R 20Mpix has a 2.4 um pixel but higher read noise. Optimal exposure conditions are Gain 30-36 dB,  -15C, 100-300s exposure, with at least 10 frames producing a total noise of 5-6(8it)IU. 

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The iPhone 14 Exmor RS has a 1.2um pixel and actually outperforms the Sony a7s at short exposure times, showing the impact of the latest technology. At longer exposures ISO12500, IPhone 14 24mm lens is 2x more noisy. The iPhone automatically reduces resolution to improve low light performance. At lowest light the effective pixel is 6um. 

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In extreme low light visible camera is a full frame HD video (5M pixel)  camera with a 15um pixel supporting ISO2M. 

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Shot noise https://arxiv.org/pdf/2112.05817.pdf

https://www.flir.com/discover/iis/machine-vision/how-to-evaluate-camera-sensitivity/

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Digital astrophotography

​A simple number to remember for order-of-magnitude calculations is that a magnitude zero star will yield roughly one million photons per second per square cm through a broadband filter above the Earth's atmosphere.

 https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Supplemental_Modules_(Astronomy_and_Cosmology)/Cosmology/Astrophysics_(Richmond)/07%3A_Astronomical_Spectra%2C_Filters_and_Magnitudes

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This converts to a Magnitude 15 star producing 1 photons sec-1 cm-2. Aperture area for C6 is 100 cm2 so there are 100 photons s-1 pixel-1. RGB filters pass around 25% each, so 25 photons s-1. The edge in Elephants Trunk nebula produces 2 photon s-1 pixel-1 through a f2 lens. 

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The reference Milky way pictures were obtained using a f2 lens 20s exposure and ISO2000, where  800 photons form a 80(8bit) level image or 10 photons/IU.  Nebula are clear in a stretched dynamic range Bortle 2 image, California Nebula generates 10(8bit)IU from 100 photons, Elephants Trunk 1(8ibt) IU from 10 photons.  Dark skies  such as Junction or Atacama run around 30-40(8bit) IU, with noise around 6-7IU. In Austin background can  be 4x higher. 

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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 = f#^2 / f2^2 / exposure time / ISO. 

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Moon                           1/400s  ISO200     f6      20 s-1 ISO-1     M-9 

Milky Way                         20s   ISO2000  f2   2E-5 s-1 ISO-1     M5 

Elephants Trunk edge  100s   ISO                                               M15

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The strategy for dim objects is to use the maximum exposure (max photons) without blurring; stationary, scanned unguided, or guided depending on the asecs pix-1 of the optics.  The ISO or gain is adjusted so that background is no more than 50-60 IU. Stack 10 -100 frames to maximize S/N by square root of the stack.

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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)IU levels.

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Elephants Trunk edge forms  20(12bit) IU change at f11 exposure 100s ISO800 or roughly 2 photons pixel-1. In a f2 lens these conditions deliver 60 photons pixel-1. 

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In 2023, the used price for the base a7s is $600 The a7sII is primarily software $800. The a7sIII has an improved BSI sensor and is around $2500, however the reviews suggest the noise improvement is marginal.  Mechanical shutter seems to be weak link 10-20K is the 90% confidence,  100K 50% confidence. I probably use 2K a year.

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Astro  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.

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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.

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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.

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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.

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Spectrum filter

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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.

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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. 

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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. 

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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!

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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. 

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Bias -  Black out scope, single short exposure time frame

Dark - Black out scope , same exposure time and time/temp as images. Need at least as many darks as lights to avoid noise amplification. 

Flats - White T shirt plus lap top, adjust exposure time to 125 - 175 IU. 

Dark flats - darks at same exposure time as Flats. 

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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 compressed video which is automatically compressed. 

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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. Cold night skies in Austin produces 3/5 or 1-2 asecs of seeing. 

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t0 is known as the coherence time and it is equals to the time interval over which the rms wavefront error due to the turbulence is 1 radian, or lambda/(2*pi), roughly lambda/6. In short this is the time over which the image of a star can be considered frozen (constant tilt/tip values, other higher order aberrations may still exist though). A very short exposure time is key to success. 

https://www.innovationsforesight.com/education/astronomical-seeing-tutorial

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Remarkable results with a 400mm aperture Dobsonian 0.3asecs Rayliegh 0.06 asecs/pix - lucky imaging 10x2 min exposures. Each 2 min was collected at 70fps using Uranus C camera, best 15% selected, Seeing = 3 (2asecs). The groups of 10 were de-rotated. In total, 200K collected frames, 10K selected compressed frames, so 100x noise reduction for random noise. Edge resolution = 0.2 asecs would be consistent with 2 asecs seeing noise. Major Cassini gap 0.6asecs clearly resolved. 

https://www.astrobin.com/6x3x3j/utm_source=astrobin&utm_medium=email&utm_campaign=notification&from_user=191491#c1162288

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C14 SCT - Rayliegh res 0.32 asecs. Exposure at altitude observatory Peru. Measured edge after sharpening 0.18 asecs. 

https://www.cloudynights.com/articles/cat/cn-reports/deep-sky-lucky-imaging-r3220

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C5 SCT - Rayliegh resolution 0.92 asecs, can resolve Cassini Gap after sharpening. 

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​Balance sampling noise for short exposure/high gain against lucky sampling. Align gains a bunch, lucky sample an additional 20%. 

Guidelines - time <10ms, G<300, 10% sample.

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For longer exposure,  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.

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Example of using a guide camera to image Stephans Quintet a Mag 14 galaxy cluster. Lens a C11 SCT f10, 80x3min = total 4 hrs exposure in a Bortle 4 using a OAG for guiding. With a C6 f2 lens could be 120 mins. Another example exposure 350x120s  = 11.5hrs, gain 10, -10c, bin1,  Bortle 5 sky.

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Narrow band imaging 

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148 hrs with f2 telescope in Bortle 7/8 S Germany

Telescope: Celestron RASA 11″ V2   6 asec/pixel -3x3pix resolution = 18 asecs
Camera: QHYCCD QHY268 M  - 3.76um pixel 6280*4210 APS-c format.
Mount: iOptron CEM120, iOptron CEM60
Filters: Baader RGB, Baader H-alpha, O III (Highspeed), IDAS LPS-P2
Software: Adobe Photoshop, PixInsight, N.I.N.A. 

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IR cameras

Warm blood 36.5C   Wien’s law   λmaxT=2.898×10−3 m⋅K  Human = 9.7um Snow =8.6um, Si threshold 1um. Smaller bandgap cameras need to be cooled. InSb to 5um.  Suitable materials are for example mercury cadmium telluride (HgCdTe, MCT) (suitable even well beyond 10 μm) and indium antimonide (InSb, up to ≈5.5 μm). temps as low 135K (-140C) required. Glass optics do not work - greenhouse effect. 

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Fused quartz  infrared transmission is limited by strong water absorptions at 2.2 μm and 2.7 μm.

"Infrared grade" fused quartz (tradenames "Infrasil", "Vitreosil IR", and others), which is electrically fused, has a greater presence of metallic impurities, limiting its UV transmittance wavelength to around 250 nm, but a much lower water content, leading to excellent infrared transmission up to 3.6 μm wavelength. 

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A SCT telescope with prime focus camera, should operate down to the Si threshold at 1um, and even a InSb camera up to 5um. 

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Cut off at 720nm gives decent color rendering. Full Astro mod down to 1um gives overwhelming red cast in daylight. 

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