Efls for imaging the LCROSS impact

[cano...@yahoo.com]

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&c=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_8UT_SP_verD_label_kaf.jpg
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

[Derek C Breit]

The following is amateur work product. Criticism and corrections are
appreciated.

---------------------------
 
We'll see..
 
Let me cup my hands to my mouth and say loudly.. (VIDEO!).
 
1.. Not once did you mention Lowlight video cameras, as used by us Occultationist to record dim stars against the lunar limb. Sometimes there is some bright limb in the FOV, sometimes not.. These are inherently well suited to this type of event. This setup is already used to record "lunar impacts" from meteoroids and such, Total Occultations, and Grazes..
 
and 2..
 
I will use my 12 f/10 and "half inch" Watec video camera at f/6.3 w/ 0.0167s exposures.
Focal length is 1920mm.. I may even go to f/3, but things have worked pretty well lately at f/6. This setup, which is well baffled and flocked, gives me mag 7 stars within 5 arcseconds of a full Moon EASILY and mag 9+ on ~77% lit moon near the bright cusp.
The mag 6.9 graze thru my front yard tonight will be recorded, no problem.
 
and 3.. My short, sensitive, 1/60 second exposures can alwaysbe stacked and stretched after the fact..
 
Derek
Morgan Hill, CA
 



 
> Date: Tue, 8 Sep 2009 15:15:44 -0700
> Subject: [LCROSS_OBS: 1030] Efls for imaging the LCROSS impact
> From: cano...@yahoo.com
> To: lcross_ob...@googlegroups.com

[cano...@yahoo.com]

On Sep 8, 4:51 pm, Derek C Breit <breit_id...@hotmail.com> wrote:
<snip> Let me cup my hands to my mouth and say loudly.. (VIDEO!).
<snip>

Thanks Derek for pointing out the omission. There was no intent to
slight the occultation community. Presence makes the heart grow
fonder. Since I do not own a low-light video, it is not at the
forefront of my thoughts when writing.

Not everyone will be using low light video. I also took the
Imagesource models to be representative of that class, since their
performance characteristics, including their 60 fps capture rate, is
similar to video.

What is the pixel element size of your Watec or the model name?

As an expert on low light video, what models do you recommend?

Was your April occultation video made at an efl of 1920mm?

http://www.poyntsource.com/tmp/April_25th_2007_Graze.mpg

Clear Skies - Kurt

[Derek C Breit]

OK.. Let's see.. (It's OK Kurt! I don't have imaging so it's not at the forefront for me either!)
 
Imagesource cameras.. Wish I had one.. I see them as a cross between a cooled CCD and a webcam. Video to me is always interlaced.. NTSC or PAL..
 
There are various video cameras, but it has been narrowed down to two for Occultations..
 
The PC164EX2.. Economical, low noise, and sensitive. Weird star shapes possibly affecting Science and not so good for imaging I would. 1/3" chip..  Sony HAD or SuperHAD.. Someone knows here I am sure.. No manual controls..
 
*THE* video camera to use for this is the Watec 902h2 Ultimate.. More noisy than the PC164EX2, but it would be the overwhelming choice for Lunar Occultations due to a huge array of manual controls..
Shutter speed 1/60 - 1/100,000 sec
Adjustable Gamma
Auto or manual gain
and a 1/2" chip / larger fov..
Not so economical at around $320
 
 
My camera is a Watec 802h board camera. 1/2" chip and about as sensitve as a regular PC164. Adjustable shutter speeds, Gamma, and Gain of off Low or High..

 
> Was your April occultation video made at an efl of 1920mm?
>
> http://www.poyntsource.com/tmp/April_25th_2007_Graze.mpg
 

That would have been much nearer to f/3, but with an 1 1/4" style focal reducer. Actual focal length unknown. I only know the focal length now because I tried my ST7* on the scope. I doubt I will change this, becase now it uses a "fullsize" reducer in the hidden cavity of my Van Slyke focuser and is at f 6.299. This is much more sensitive than before. Apparently I was obstructing the light path with the small FR..

Derek
 
* The ST7 (ABG.. Parallel Port) is for sale or trade. I would like to trade an imager for a NON ABG parallel port ST7..
 


 
> Date: Tue, 8 Sep 2009 16:40:00 -0700
> Subject: [LCROSS_OBS: 1033] Re: Efls for imaging the LCROSS impact
> From: cano...@yahoo.com
> To: lcross_ob...@googlegroups.com
>
>