VISUAL
ASTRONOMY
Count the Pleiades
an investigation
into the visual detection of objects at the eyepiece...
As
a small child I remember being driven back to Portland at night after a
visit to relatives in the countryside. I laid in the back of the
station wagon, peering up at the sky through the rear window. The stars
were so brilliant against the darkest black of skies! It hurt my eyes
to look at the brightest stars! What a contrast to the washed out city
skies of Portland, even in 1960!
Since most
astronomical objects are quite dim as seen through the eyepiece, it
behooves us to understand the conditions that permit the best
visibility. In the retina, light is focused onto cylinder shaped rod
cells and cone shaped cells, initiating a photochemical process that
results in an electrical signal to the brain. Light sensitive
molecules, called chromophores are held by proteins. During darkness, a
protein called rhodopsin, in a pigment called visual purple,
accumulates in the rods. The amount of visual purple determines the
sensitivity of the eye to light, and mostly reaches maximum after
thirty minutes, with some improvement of up to two hours. Cone proteins
are very similar to rhodopsin, in fact, differing in only one key amino
acid. This single difference in the amino acid at position 122 results
in the cone proteins resetting 100 times faster than rhodopsin after
absorbing light. Visual purple sensitizes our eyes by many thousands of
times. The change in light sensitivity when the iris opens and closes
is very slight in comparison.
In greater detail:
Rod cells are long hot dog affairs about 1/125 inch long with the
synaptic and nucleus end towards the incoming light. Each rod
cell contains 2000 stacked disks which contain up to 100 million
modules of light sensitive pigment rhodopsin. Each rhodopsin
molecule has two parts, the opsin protein and the light absorbing
substance retinal, derived from vitamin A. Before light hits
it, the retinal is in the isomer form 11-cis-retinal. When a
packet of light energy is absorbed by rhodopsin, it twists
11-cis-retinal to form another isomer, all-trans-retinal.
This changes the configuration of the opsin protein converting the
whole molecule from rhodopsin into metarhodopsin II in 1/1000
sec. Each metarhodopsin II molecule activates hundreds of
molecules of transducin, a protein. Each of these activates
an enzyme, phosphodiesterase, which alters the structure of thousands
of molecules of the neurotransmitter cGMP, cyclic guanosine
monophosphate. Levels of cGMP which in darkness are high, are
thus reduced, closing channels which allow sodium ions to flow through
the cell membrane. cGMP's function is to keep these channels
open. In darkness, these open channels allow the flow of
positively charged sodium ions, called the dark current, to counter the
diffusion of positive potassium ions out of the cell, making the inside
slightly negative. When light hits the rod cell, sodium entry
is reduced, charging the cell's interior more negative, called
hyperpolarization. Hyperpolarization reduces the release of
neurotransmitters from synaptic vesicles, resulting in signals being
sent to the brain. All chemicals are cycled within 1/5
second. Rods and cells form the retina's outer
layer. Within this layer are incredibly complex layers of
interconnected neurons. Hundreds of rods and cones feed into
a dozen or so bipolar cells, which then signal a single ganglion cell,
carrying out what might be called data compression. The
ganglion cell's firing rate is determined by the sum of the signals
from all of its photoreceptor cells, the rod and cone cells.
130 million rod and cone cells are compressed into 1 million ganglion
cells in the retina. Nerve signals from these 1 million
ganglion cells travel along the optic nerve to the cross over junction
called the optic chiasma. The signals continue onto part of
the thalamus known as the lateral geniculate nuclei (LGN).
They then continue onto the visual cortex of the occipital
lobes. The main reception area here is called V1, essentially
a replica of the retina. Areas V2 and V3 separately process
various aspects of vision like shape, color and movement.
These areas communicate with other cortical areas including the
temporal lobe and the language center. Here we become
consciously aware of what we see. Pathways from the LGN also
bypass V1, connecting to the brain's motor system, making it possible
to sense and react to visual signals without the extra time needed to
become consciously aware, this is called blindsight. Other
subconscious pathways include the superior colliculi which cause the
visual startle reflex to anything unusual.
The eye's
response is multi-phase. See http://webvision.med.utah.edu/light_dark.html
Astronomers measure brightness in units of
magnitude. The eye roughly follows a logarithmic response, with a
magnitude equal to a change in brightness of about 2.5 times. A
difference of five magnitudes equals a change of brightness of 100
times.
Rod cells are about four magnitudes more
sensitive to light than cone cells. Cone cells are concentrated in the
very center of the retina, with rod cells reaching a peak concentration
at 20 degrees off center and tapering to half their numbers at 60
degrees off center. Interestingly, rod cells are a bit more
concentrated away from the nose. This leads to the following graphic,
which shows where to best place a dim object for observation in the
eyepiece. You will want to look at a point about 15 degrees away from
the object, slightly above it and with the object aimed at your nose.
Increasing aperture concentrates more light into the star
image,
hence making it brighter. Here is a table of aperture and magnitude
values, from a Sky and
Telescope
magazine article table published elsewhere on the net:
Telescope Limiting Magnitude
Aperture
Probability of Detection
Inches
98% 90%
50% 20%
10%
5% 2%
1
9.7 10.2
10.7 11.2
11.7 12.4 13.2
2
11.2 11.7
12.2 12.7
13.2 13.9 14.7
3
12.1 12.6
13.1 13.6
14.1 14.8 15.6
4
12.7 13.2
13.7 14.2
14.7 15.4 16.2
5
13.2 13.7
14.2 14.7
15.2 15.9 16.7
6
13.6 14.1
14.6 15.1
15.6 16.3 17.1
7
13.9 14.4
14.9 15.4
15.9 16.6 17.4
8
14.2 14.7
15.2 15.7
16.2 16.9 17.7
10
14.7 15.2
15.7 16.2
16.7 17.4 18.2
12.5
15.2 15.7
16.2 16.7
17.2 19.9 18.7
14
15.5 16.0
16.5 17.0
17.5 18.2 19.0
16
15.7 16.2
16.7 17.2
17.7 18.4 19.2
18
16.0 16.5
17.0 17.5
18.0 18.7 19.5
20
16.2 16.7
17.2 17.7
18.2 18.9 19.7
22
16.4 16.9
17.4 17.9
18.4 19.1 19.9
24
16.6 17.1
17.6 18.1
18.6 19.3 20.1
30
17.1 17.6
18.1 18.6
19.1 19.8 20.6
36
17.5 18.0
18.5 19.0
19.5 20.2 21.0
For extended objects, things are not so simple. For starters,
it is not possible to increase the surface brightness of an extended
object by increasing the aperture. An example: take an object of 10
magnitude/ square arcsecond as seen by the unaided eye at night, exit
pupil open to 7mm. Now, look at the object through a 10" scope. If
there is no magnification to the image, the surface brightness will
increase by the ratio of the scope's aperture to the eye's aperture
squared, or, (10"/0.3")^2 =~ 1000x. However, in order to fit all of the
light from the 10" aperture into the eye's exit pupil, we must use at
least 33x. 33x will dilute the image brightness by 33^2 =~ 1000x, so we
are back where we started. In fact, because of mirror coatings not
reflecting 100%, and the small obstruction caused by a diagonal, the
image brightness per area will actually be a little less than with the
unaided-eye!
This leads to the
interesting conclusion that sky background brightness as seen in the
eyepiece is entirely dependent on exit pupil. At a given
location on a given night, no matter the size of scopes, if they are
giving the same exit pupil, then the sky background brightness will be
very similar.
So how can we see the object in the
scope? The eye is a marvelous detector of low contrast faint objects,
but the light must fall on large numbers of rod cells so that the
eye-brain can detect the slight contrast difference between object and
background. The slighter the contrast, the more rod cells that the
object's light must fall on in order to generate a signal difference
between object and background. By increasing the telescope
magnification, the object is magnified so that its light falls on many
rod cells. The ratio of brightness between object and background, or
contrast between object and background, stays constant because the
increase in magnification that dims the object also dims the sky
background in equal amounts. The best magnification to detect an object
is the magnification that gives the best eye detection contrast value
for a given apparent object size and sky background.
The
first and still best reference on visual astronomy is Clark's book, titled "Visual
Astronomy of the Deep Sky". It is a marvelous book, and is
worth many readings. Clark has added additional comments since the
book's publication, at http://clarkvision.com/visastro/omva1/index.html
For Nils Olof Carlin's analysis of Blackwell's
original data, please see blackwel.html.
Here, Nils shows that the best contrast comes when the background is
dimmed below visual detection, and the object is about one degree in
apparent size.
In
extensive discussions between
Roger Clark, Harold Lang, Nils Olof Carlin, and myself, it became clear
that there is more than one way to define 'optimum detection
magnification'. In fact, I steer clear of paying attention to
magnification entirely, not just on rickety department store telescopes
advertised to show the splenders of the sky up to 675x! The eye does
not have magical powers to discern what magnification you are currently
using.
The
eye, however, does react differently depending on exit pupil - the size
of the disc of light formed by the telescope's optics. Sometimes called
a Ramsden disc, only light passing through this disc from the telescope
can be seen by the eye. In fact, the exit pupil is the image of the
aperture stop, or cylinder of light that the telescope's optics takes
in. Large exit pupils occur at lower magnifications and smaller exit
pupils occur at higher magnifications.
The eye's ability to
detect objects depends on a mix of exit pupil, sky background
brightness, object brightness and object size. For instance, narrowing
the exit pupil (going to higher magnifications) means dimming the sky
background brightness and increasing the apparent size of the object,
whilest dimming its surface brightness. So what's easier to detect - an
apparently small sized object on a brighter background or an apparently
larger sized but dimmer object on an even dimmer background?
For
possible answers, we can turn to Blackwell's data as presented by Clark
in his Visual Astronomy. Departing from the usual path of calculating
the ability to detect the object at various magnifications, let's look
at other presentations of the data that are quite revealing.
First,
let's explain the concept of sky background brightness. The night sky,
even at very dark sites, glows faintly due to zodiacal light and
airglow. See Brian Skiff's discussion at http://www.astropix.com/HTML/L_STORY/SKYBRITE.HTM. You can measure the darkness (or brightness) of your night using a sky glow meter available at http://unihedron.com/projects/darksky/.
Dark sky sites have readings close to 21.5 magnitudes per square
arcsecond. Observing through a telescope with your eye's pupil fully
opened results in a sky background glow in the field of view equal to
that of the night sky. Magnifying the image results in smaller exit
pupils, the useful maximum magnification or smallest exit pupil being
close to 1mm. The sky background brightness drops more than 4
magnitudes to close to 26 magnitude as exit pupil shrinks to 1mm.
The eye's detection ability with sky background brightness values from 21 to 26 is:
From
the chart we can see that large exit pupils result in the best ability
to detect objects over a wide range of apparent sizes. As the exit
pupil shrinks, the ability to detect objects declines and becomes
concentrated on apparent sizes of a degree or two. We can see this by
plotting best apparent detection size against declining sky background brightness.
There are several factors in increasing the detectability of an object, or the contrast of the field of view.
- Most
important is to observe in the darkest skies possible.
- The single biggest factor in contrasty views is proper
baffling of your telescope to prevent stray light from fogging the
eyepiece. It's a popular but mistaken belief that optical quality
influences general contrast in the field of view - it doesn't. For
Newtonians, at a minimum, use a focuser baffle, a diagonal baffle and a
primary mirror baffle. Test the scope's baffling by shining a
flashlight around the scope at night while looking through a low power
eyepiece. You shouldn't be able to tell when the flashlight is aimed at
the scope. When
you look through the focuser with the eyepiece removed, you should only
see optics and blackness.If in city lights, block them from your
observing site - the inability to dark adapt in the city is the biggest factor in hampering city viewing.
- Make sure you eat healthy with sufficient
vitamin A, do not smoke, do not drink, give yourself two hours to dark
adapt, and avoid bleaching your eyes by avoiding bright direct sunlight
for a day or two beforehand. Avoid momentary lights except for the dimmest
possible.
- Put a black cloth over your head when at the eyepiece.
Memorize as much as possible so that you don't have to read charts or
books during the evening.
An
important factor is the exit pupil. Large exit pupils mean low power
mean wide angle views with the brightest sky background. Small exit
pupils mean high power narrow field views with the dimmest sky
background. The best exit pupil depends on sky background brightness,
object magnitude and size. We can arrange the Blackwell data to show
best contrast detection levels at a range of exit pupils.
Here's
a fairly dim large object, the California Nebula. Aperture makes a
significant difference in ability to see the nebulosity. The ability to
detect the object is decreases a bit as the exit pupil tightens. Since
the object is large, it's best to stay at a large exit pupil.
Next
is a very dim small object, the Horsehead. The detection level is much
closer, almost undetectable. Aperture makes a major difference. Note
that the greater aperture is able to tolerate smaller exit pupils
(higher magnifications) better.
Now
a favorite low surface brightness hard to see edge on galaxy, NGC 891
(the Outer Limits Galaxy). The best combination is the larger aperture
at 3mm exit pupil. This is an example of experienced observers
reporting that, given sufficient aperture, many objects (or detail in
objects) are best seen at smaller or medium-high magnification. This
also illustrates why this galaxy is surprisingly challenging in an 8
inch scope.
Finally
a small faint galaxy, NGC 1275, one of the two anchors of the
Perseus Cluster of Galaxies. The larger aperture does best at
largest exit pupil, lowest magnification. The smaller aperture does
better at a mid-range exit pupil (medium magnification).
Try the online visual detection calculator.
Bill
Ferris has generated a series of ODM matrices that compare the
variables with each other: http://members.aol.com/billferris/odm.htm
EOD