The Sun has a brightness of -27 and very faint stars are +24, +30 for the Hubble.
The unaided night adapted human eye can see down to Mag +6.

The above results in this formula:

Visual Magnitude = 2.5 * Log₁₀(# of eyes) + 6                                                        Eq 1

The 2.5 value comes from Log₁₀[100 ^(1/5)] the definition for star magnitudes.
The 6 is the magnitude seen from 1 eye.
# of eyes is (light gathering area) / (area of night adapted eye) = (PI * D² /4) / 0.059651 [inches]
For a 7 mm pupil diameter, # of eyes = 13.16 * D²  [inches]

Note: In the Edmund Scientific book "all about Telescopes" the # of eyes is given as 9 * D².
This must have been based on practical observation through the telescopes of the time, either poor transmission in refractors or the central obstruction in reflectors.

Visual Magnitude = 5 * Log₁₀( D ) + 8.8                                                                Eq 2

Where D is the diameter of an unobstructed primary in inches

The results of this equation match the faintest star magnitudes shown in "all about Telescopes" and is based on first principles.

I have heard that the constant adder should be 10.0 for dark skies and at about 1,000 foot elevation.  A more accurate equation would contain a term that used elevation as an independent variable, i.e. the higher you are the fainter a star you can see.

Human Eye

The human eye has a max pupil diameter of 7 mm and a physical diameter of about 3.6 cm.  If there are 120 million rods (intensity detectors, pixels) spread over 1/2 of the sphere. The 1/2 sphere has an area of 2*PI*r*r or 2035 sq mm.  The area divided by the number of rods gives 16.7 micro meters pitch for the rods.  If the rods are touching each other the eye could be thought of as having 16.7 micron pixels.

A rough approximation is that the f number of a scope is it's primary focus spot size in micro meters so . . .If a scope has an f number greater than 16.7 then a star image may be larger than a single rod.

9 July 2007 - I don't think the rods and cones are spread out over half a sphere.  It's more like 1/8 of the sphere, i.e. a 90 degree viewing angle.  Area (sq mm) of sphere the size of an eye = 4*PI * (36/2)^2 = 4071 sq mm divided by 8 is 508 sq mm.
Dividing the active area 508 sq mm by 120 million gives 4E-6 sq mm per pixel.  Each sq mm contains 1E6 sq microns so the area of one pixel in microns is about 4.

This is why low f-ratio telescopes (like f 4 scopes) produce star images that have more detail than scopes with higher f-ratios.  Also I don't think the rods and cones are spread over the active area in an even manner, but rather they are bunched up more in the center with a decreasing density as you move away from the center of the field of view.

Applying the formula for a 4" refractor gives a visual MAG = 11.4

The same 4" refracting scope (no central obstruction) as above now is fitted with the StellaCam EX running at 128 frame* integration.
The central star in M57 is visible in the StellaCam EX which is a MAG 15 star.
The improvement in seeing is 15 - 11.4 = 3.6 magnitude numbers.

To predict how the StellaCam EX will see, add 3.6 to the visible magnitude for the same scope.

StellaCam EX MAG = Visual MAG + 3.6                                                Eq 3a
StellaCam EX MAG = Visual MAG + 2.6                                                Eq 3b

Eq 3a differs form Eq 3b in the reported improvement of the StellaCam EX that may be due to factors not yet taken into account.  The average improvment is 3.1 in magnitude.

* An American EIA B&W TV image is made up of a series of fields taken at a rate of 60 Hz.  Two fields make a frame so the use of the word frame above is not technically correct, it's field integration. At least 2 fields should be integrated (added) to get the full resolution of the camera.  The fields are interlaced so adding two fields does not add any information it just combines the two interlaced images into a single frame.

An integration setting of 128 results in an exposure time of 128 * 1/60 = 2.13 seconds.

12" SCT with 3" dia secondary mirror
active area = PI * 6 * 6 - PI * 2 * 2 = 100.53 sq in
# eyes = 100.53 / 0.0596 (7 mm area in sq in) = 1685.31
Using Eq 1 above gives Vis mag = 14.1
To use Eq 2 convert the effective light gathering area (100.53 sq in) back into a diameter of 11.31", gives 14.1
reported seeing mag 16.7 stars with StellaCam EX or 2.6 magnitudes dimmer.

To see MAG 12 stars with the StellaCam EX choose a scope to see visual MAG 8.4 stars (12 - 3.6).
D = 10 ^ (MAG - 8.8) / 5

D = 10 ^ ( 8.4 - 8.8) /5 = 0.83"

Since the common camera lens specification is the focal length and "f" number the objective diameter needs to be computed.
"f" = (Focal Length) / (Objective Diameter) in the same linear units, like mm.
A number of lenses are offered for the StellaCam EX :
 

FL mm	f	Obj Dia mm / inch	FOV V x H x Diag	Visual MAG	SC EX MAG 128 field	SC EX MAG 2 field
2	1.4	1.4 / 0.05	180	2.5	6.1	4.6
4	1.4	2.9 / 0.11	62 x 77 x 90	4.1	7.7	3.2
6	1.4	4.3 / 0.17	44 x 56 x  67	4.9	8.5	4.0
8.5	1.3	6.5 / 0.26	35 x 46 x 56	5.9	9.5	5.0
12	1.2	10 / 0.39	23 x 30 x 37	6.8	10.4	5.9
16	1.4	11.4 / 0.45	17 x 23 x 28	7.1	10.7	6.2
25	1.3	19.2 / 0.755	11 x15 x 18	8.2	11.8	7.3
50	1.3	38.5 / 1.151	6 X 7 X 9	9.7	13.3	8.8
75	1.4	53.6 / 2.11	4 x 5 x 6	10.4	14.0	9.5
145	2.5	58.0/2.28	1.9 x 2.5 x 3	10.6	13 to 14*	8.5 - 9.5
300	4.0	75.0/2.95	1 x 1.25 x 1.5	11.2	14.7	10.2

*reported from actual setup in S. Africa
Visual MAG means if the lens was used to build a telescope and stars viewed with a human eye.

Feb 2008 - Note that when a 35 mm film camera lens is used you can get a large objective diameter without a long focal length, for example a 50 mm FL is the "standard" lens for 35 mm film and an f/1.4 is common yeilding 35.7 mm objective diameter.

Effect of Integration in StellaCam

Brightness

If the 50 mm lens is used, the StellaCam EX should see down to maybe mag 12.8 at 128 frame integration. If the integration is set to 2 (i.e. turned off) then the star brightness will be reduced about 64 times.  Remember that 2 fields make up one frame.  Since mag numbers change by 5 for a 100 times change in brightness then the 128 field (64 frame) StellaCam EX should see mag 4.5 less or 8.2 stars.  This is better than the human eye.  The following table is based on no noise being present at any of the integratoin levels.
 

Field Integration	Frame Integration	Mag Improvement Eq 1(Frame Int)
2	1	0
4	2	.8
8	4	1.5
16	8	2.3
32	16	3.0
64	32	3.8
128	64	4.5

The 12.0 mm FL f 1.2 lens running with 1 frame (i.e. at 2 fields) integration should have about the same sensivity as a human eye.
Since the objective diameter of the 12mm f 1.2 lens is 10 mm it is 2 eyes and applying Eq 1 says that the chip is 0.8 mag less sensitive than the human eye.

Integration Not good for Seeing Satellites

 If an object, like an Earth satelite or meteor is moving quickley through the field of view its brightness will not be magnified by integration but instead reduced.  This is becasue the satellite will appear on different pixels at different times during the integration.

9 July 2007 - But this is not always the case.  For geostationary satellites the relative movement of the satellite is very slow so integration will be very helpful.  If a satellite tracking mount is being used integration will also be good.

Note on Mounts for Satellite Viewing

The common astronomy mounts are either elevation over azimuth or polar.  In both cases movement in both axis is needed to track a satellite.   If you are trying to image the satellite (rather than see it as a dot) then field rotation is also needed in both cases.  In the case of El/Az mount there is a dead spot at the zenith since it takes some time to make a 180 degree Az move.

A better mount would, for lack of a known to me name, be called a satellite polar mount.  The idea is that the scope polar axis is aligned to be at right angles to the plane of the satellite.  The satellite declination is set to a small negative angle depending on where you are on earth and a single satellite right or left hour angle motor running at a constant rate will track the satellite.  If it is the type that's always pointing at the earth, then it's image will not change orientation during the pass and no field rotation will be needed.

This may be called a four degrees of freedom mount as opposed to the common two degrees of freedom mounts used for astronomy.  At the base could be an El/Az mount programmed to point parallel to the central axis of rotation of the satellite.  Around the axis defined by the El/Az mount the orbit tracking motor would rotate the scope either clockwise or counterclockwise as needed at a rate depending on the orbit height.  Since orbits are elliptical there would be small changes in rotation rate needed.  The forth axis is for the small satellite declination.  This may or may not be needed to be programmable since it's always going to be some small fixed angle since we are not at the earth's center.

Noise

If there were no noise then you could integrate as many times as you liked and could see as faint a light as you choose, but there is background noise.  As the noise is integrated it's brightness increases and will eventually be at the maximum white level.  The Mintron 12V1 (StellaCam EX) use a 10 bit Analog to Digital converter so if 1024 fields (2^10) were integrated any noise at the 1 bit level would turn into white.  128 field (2^7) integration will bring any noise at the 3 bit position (count of 15) to white.  This works well when the sky is less than a count of 15 out of the A/D converter.

Hot Pixels

The StellaCam EX has some number of hot pixels that will appear as stars.  The number of hot pixels increase as the ambient temperature increases.

There are some things that can be done to overcome the fake stars:

• multiple frames can be stacked using a non tracking mount.  This way the real star field appears in a different part of the frame and stacking adds the real stars and averages out the fake ones.  Some adjustment of the frame integration may be needed to avoid star trails.
• For satelite, NEO, astroid viewing frame subtraction will remove real and fake stars that are fixed in the frame of a tracking mount.
• CPU Fan Modification - use a CPU fan mounted with Velcro to the camera (requires curring big inlet hole and drilling a number of outlet holes into the camera cover, and appears to reduce the false stars.  Based on the October 2002 Sky & Telescope.

You might want to temporarily attach the fan to the camera body with tape while the camera is mounted to the scope to check for clearance as the scope points in different directions to avoid interference.
Feb 2008 - I've read that most of the noise is caused by the imaging chip and cooling will not reduce it.

Imaging Chip

The Sony ICX038DLA.  768x494 active pixels each of which is 8.4 x 9.8 um.  spectral response peaks at 500 nm. is the NON EX chip
Sone web page about EXview HAD CCD -
EXView HAD CCE chips are:
ICX248AL - monochrome
ICX249AL - color

Mintron

Mintron makes a number of TV cameras designed for the security market that are optimized for both daylight and very low light conditions.  As the scene gets darker and darker the camera starts integrating frames.  There's speculation as to whether they integrate on the 1/2" CCD chip or if the DSP in the camera is integrating individual fields, but in any case the camera starts out with a very sensitive Sony HAD EX type CCD.  The Black and White (more properly called gray scale) 12V1EX is the most sensitive camera and the color version, although ot as sensitive also gets good reviews for astronomical use.

There are two ways that people use these for astronomy.

Real Time

In this mode the output of the camera is fed to a CRT type TV monitor (lap top or LCD screens are not as good for this) that has high resolution (over 600 lines) and that has manual brightness and contrast controls.  The resulting image as seen by the human eye is as good or better than the images that can be obtained by the second method.  A scope used this way has a multiplier of about 3 times on is objective diameter for what can be seen when compared to the unaided eye.  Some feed the video to a monitor at the scope and also into their house so friends and relatives can view from the comfertable indoor space.  Others remotely control the scope and observe from indoors.

Post Processed

The output from the camera is recorded on a TV recorder, mini DV is preferred, SVHS is the second choice and a plain VHS is OK if that's all you have.  A few minutes of video is fed into a computer using a video capture card (this is different from a frame capture card).  Then bad seeing frames are discarded and the good ones are aligned and stacked.  This may be combined with dark field and flat field corrections and gamma adjustments to yield a still image.

V  Series  Star Light cameras - they have a number of 1/2" image chip models: 12V1is the 1/2" B&W, 62V1 is the color.
The Super Circuits  P-38 is one of the 1/3" Color 0.008 Lux Sense-Up type integrating cameras, is the 63V3 with motion detection and full RS-232 to set and read ALL parameters.  The RS-232 uses the ack/nak protocol.

For sattelite searching the integration is not needed and a lower cost camera like the 1/2" CCD, high-res  OS-40 or
MTV-1802CA may be a better choice. 12V1 web page in German - Babel Fish web page translation
Mintron for IRAM - Detlef Koschny
Testing the Mintron camera - Detlef Koschny

Larry's Astro Videography -  Astrovid Stellacam EX CPU Fan Modification!!! - Test Results -

SAC/Mintron

Watec

The 120N (Stellacam II) is a newer camera than the Mintron 12V1EX and has longer exosure times, up to 8.5 seconds for the U.S. version and so is more sensitive.  But it does not have fast shutter speeds, so needs ND filters for planatery or other bright subjects.
Uses the Sony ICX418ALL in the U.S. 60 Hz  and the ICX419ALL in the 50 Hz version

The Watec WAT120NRC video camera - The first comparison review
Comparing two potential meteor cameras – the Mintron and the Watec 120N - second comparision, does not agree with first review.

ASTROVID

Astrovid has been a pioneer in the TV imaging area for a number of years.
The original Astrovid 2000 camera was just a sensitive TV camera with modifications to allow control of the image brightness and gamma and there was an optional external image integration box.  The Stellacam (Mintron 12V1) combined a camera with image controls and integration into one box. The StellaCam Ex (Mintron 12V1EX, uses the more sensitive EX CCD chip), and the Stellacam II is the Watec 120N.

Astrovid also offers a modified 12V1xx camera with RS-232 remote control capability.
Web page showing their cameras and the chips in them.

Mallin Cam

Super Circuits

f Number and Pixel Size

Spectral Response

Links

24/7 Sky-Weather-Astronomy web cam
my Astronomy web page
my Binoculars we page
my CCD Astronomy web page
Long Exposure modification for the 1004x ExView CCTV board camera by  Jon Grove - anti blooming
Collected Data and Links on Low Light CCD Camera's in Amateur Astronomy -
AstroGeek's StellaCam EX web page
Yahoo StellaCam EX Group listserver now back to the VideoAstro group -
ITE sells the "EX" as their Deep Sky Pro TV camera
Polaris USA sells it as their model DXB-8200SL for $360
Video Surveilance Cameras & Video Astrophotography -
Supercircuits PC-23C -> PC164C -> KPC-350BH  - these would be better if  they had manual controls for gain & gamma.
Black Box  Camera - Precision GPS OSD Time Inserter - uses PIC 16F628 (with the now obsolete?) STV5730A OSD chip
MetRec  (Meteor Recognizer) - Software that captures Meteors viewed by a TV camera, needs the Matrox $600 MeteorII frame grabber. -  Yahoo MetRec Group -
Video Capture Astrophotography - Sensivity Comparison Test - Sony ICX248AL HAD EXview CCD & Sony ICX038DLA HAD CCD
Skycam Vechta - Daytime web cam & Night Time sky cam
Sirko Molau - Video Observations of Meteors: History, Current Status and Future Prospects -
Filter Thread Mounted 0.6 Focal Reducer -Steven Mogg - used inside the 1 1/4" to c-mount adapter
JAI CV-M50IR - uses the same Sony 1/2" chip as the 12V1EX (Pixel Size 8.6 x 8.3 microm)  Can be controled by the Video Star for long exposures. Video Star works with the FlashBus MV/Pro frame grabber
The Most Fabulously Useful Formula In Astronomy -
Some Notes on the Matter of Matching CCD Camera Pixel Size to the Capabilities of an Instrument -
Pixel size and field of view - (plate scale (radians/meter)) = (1 radian) / (Focal Length meters), f# = (Focal Length) / (Objective Daimeter)
Telescope Optics & Pixel Size -
experiences with cameras for astronomy has info on a number of TV cameras used with scopes
Night Sky Live - probably uses an image intensifier, but maybe this could be done just using a Mintron or Watec type camera without the intensifier.
Video Surveillance Cameras & Video Astrophotography - Info on some Super Circuits cameras and how to work around the auto Iris function when no auto iris lens is being used (like when the camera is on a telescope).



Matthias Bopp, DD1US - Astronomy - Astronomy Downloads- is supposed to publish details of an RS-232 option for the Mintrons
       has paper on how to replace the bright LED on Mintron with more astronomy friendly LED.
   



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