ON THE EVALUATION OF BINOCULARS FOR ASTRONOMY
The following is a discussion on the evaluation of binoculars
for astronomy.
Last spring (1989) I made the decision to purchase a giant 20x80
binocular and, in the process, to upgrade my antiquated 7x50's to one of
the newer fully-multicoated models. Both binoculars will be used
primarily for astronomical observation in the field, obviating the need
to transport my rather heavy, cumbersome scope to the site on our cold,
winter nights. Also, the 7x50 will be used in summertime to check out sky
conditions before setting up the main scope, or, simply, for general
observing.
It became clear that a precise manner in which to represent the
important parameters of any binocular model as a single value (figure of
merit, if you will) was a requirement not yet fulfilled. Unfortunately,
here in the states, distributors customarily tend not to reveal the
complete specifications concerning their product lines but rather to
accentuate the better or "fad" qualities.
After compiling a list of all consequential parameters, I was able
to derive a formula based on the denominative parameters specific to
astronomy. I have called this evaluation the FFQ which stands for
"Figure of Function and Quality for Binoculars for Astronomy." This
function reduces those parameters of a binocular, specific to astronomy,
to a unique value that can be used to compare various models.
A total of twelve terms generates the FFQ function in the formula
below. The exponential value, 10(-7), allows the FFQ to be normalized so
that its value will fall within a range of 1 to 1000 for binoculars that
are available commercially. A modest scientific calculator can handle
the reduction with ease.
When all parameters are not specified in manufacturers' product
literature, one may obtain this information by either writing directly to
the manufacturers or by visiting a local shop and inspecting the
particular models firsthand.
To illustrate the evaluation, I have carried out the reduction
(below the formula and description of terms) for two currently-available,
but notably-different, binoculars.
FIGURE OF FUNCTION AND QUALITY FOR BINOCULARS FOR ASTRONOMY
FFQ = (OBJDSQR/100 x XSQR x RB x Q x FOVSQR x %FD x PRS x %LT x ER
-7
x OELD x FOC x C-F) x 10 , where,
1) OBJDSQR/100 = DIAMETER OF OBJECTIVE LENS IN mm (millimeters)
SQUARED, DIVIDED BY 100.
This term is proportional to the light gathering power
of the objective lenses of the binocular.
2) XSQR = STATED POWER SQUARED.
This term is proportional to the area of the image;
The area of the image directly relates to the amount
of detail resolved, assuming near-perfect optics.
This term is of primary importance when choosing a
particular binocular model for astronomy purposes.
Hypothetically, however, if the optics were perfect,
and if X = 1, would such a binocular be really useful?
3) RB = RELATIVE BRIGHTNESS EQUATES TO EXIT PUPIL SQUARED.
SQUARE THE VALUE OF THE STATED EXIT PUPIL.
The exit pupil defines the diameter of the cone of
light that enters the eye. EP = OBJD/X, the diameter
of the objective lens in millimeters divided by the
power.
EP squared is, however, proportional to the area of
the exit pupil, which, under optimum conditions,
should correlate well with the area of the entrance
pupil of the eye. Due to the nature of the eye, when
the exit pupil of the binocular matches the entrance
pupil of the eye, the greatest number of photons from
the stars will be detected, and this translates
into image brightness.
Typically, too large of an exit pupil is wasteful and
does not utilize the full potential of the optics,
while too small of an exit pupil effectively dims the
image; therefore, this term is especially significant
for astronomy enthusiasts.
4) Q = TYPE OF COATING USED, NORMALLY NOT VERIFIABLE.
Q-VALUE
A) 0.50: all optical surfaces uncoated (rare).
B) 1.00: all lenses and prism surfaces fully coated
with the standard single-layer MgF (magnesium
fluoride) coating. 2
C) 1.10: similar to "B" but multicoated (at least two
separate and distinct coatings applied) on
exposed objective and ocular lens surfaces
as well.
D) 1.20: fully-multicoated on all lens and prism
surfaces.
E) 1.25: similar to "D" but enhanced multicoatings:
three or more special coatings are
applied, i.e., Fujinon's patented EBC
process of multicoating whereby up to 11
separate layers of coating are applied.
F) 1.33: similar to "E" but, in addition, special
rare-earth formulations have been used for
all lenses.
5) FOVSQR = STATED FIELD-OF-VIEW (FOV), IN DEGREES, SQUARED.
When considering true flat-field optics, the field of
view is most important. This term is proportional to
the area of the image viewed.
6) %FD = PERCENTAGE OF FIELD DISTORTION.
Calculate this term as follows:
%FD = [1 - (% of DIAMETER of FOV that
is distorted/100) SQUARED]
Examples of %FD Calculations.
NO DISTORTION, FLAT-FIELD OPTICS: [1 - (0/100)]SQR = (1 - 0)SQR = 1
50% OF FIELD DIAMETER DISTORTED: [1 - (50/100)]SQR = 0.5SQR = 0.25
80% OF FIELD DIAMETER DISTORTED: [1 - (80/100)]SQR = 0.2SQR = 0.04
This term defines the area of the FOV that average eyes
will clearly perceive as distortion of some kind, e.g.,
astigmatism, chromatic or spherical aberration,
fuzzy edges, etc.
This parameter negates any weighting caused by a very
large, but highly distorted, FOV.
7) PRS = PRISM TYPE. Determine the value of this term
as follows:
BaK-4 = 1.0 BK-7 = 0.85
special rare earth formulation = 1.22
This term is, perhaps, more of a quality judgement call
since the effect of prism choice may possibly be
absorbed by other parameters. Notice, however, that
I have chosen as the de facto standard BaK-4 prism
glass, with a weighting of unity--will not effect
FFQ value.
8) %LT = AVERAGE PERCENTAGE OF OVERALL LIGHT TRANSMISSION OVER
THE VISIBLE SPECTRUM FROM 450 TO 640 NANOMETERS.
This term is expressed as a decimal, i.e., 95% = 0.95.
Obviously this term is related to Q but is dictated
by the quality of the manufacturing process; for
example, additional reduction of internal reflections
may be achieved by coating the edges of lenses and
prisms with Carbon-Black.
The percentage is all but impossible to determine
without sophisticated instrumentation. Either take
the manufacturer's word on this, or consult binocular
assessment and comparison tests in the literature.
9) ER = OCULAR EYE RELIEF IN mm.
This term represents the practical working eye relief
in millimeters which may or may not be in agreement
with the published specification for the binocular.
10) OELD = DIAMETER OF THE OCULAR'S EXTERNAL EYE LENS IN mm.
This term, again in millimeters, predicts that a
larger diameter is beneficial. A larger diameter
usually indicates a larger exit pupil, both of which
aide in less critical positioning of the eye's
entrance pupil with respect to the center of the eye
lens and exit pupil, especially apparent during
daylight observing. OELD is another measure of
binocular quality.
Beware, however, as I suspect that an occasional lens
arrangement may employ a useless but large, plano-plano
"eye" lens (even possibly uncoated) to give the
appearance of a quality instrument, i.e., a FAKE.
11) FOC = TYPE OF FOCUS.
Individual Focus (IF) = 1.0 Designed to be impervious
to moisture penetration.
Center Focus (CF) = 0.75 Subject to internal
contamination as well
as optical misalignment.
Permafocus (NO FOCUS) = 0.01 A truly preposterous
concept which relies on
one's eyes to be perfect
in EVERY WAY in order to
achieve the desired
focus!
If an IF model is truly waterproof, is really
dry-nitrogen-filled to prevent oxidation, and is also
permanently sealed with internal desiccants to reduce
the possibility of fungus growth, then allow this term
to equate to 1.3.
12) C-F = CONSTRUCTION FACTOR.
This term is definitely a quality call; however, it
can be quite useful as well--sort of like the icing
on the cake.
A) large, fold-down rubber eye guards ....... 1.15
B) recessed objective lenses: help
in the prevention of dew formation
during nighttime observing sessions
and provide improved contrast
under all observing conditions,
but especially during the daytime ........ 1.2
C) both "A" and "B" ......................... 1.38
D) both "A" and "B" but with
contoured eye guards or
adaptability of independent
units to binocular ....................... 1.45
E) none of the above ........................ 1.0
Multiply the above result by the
appropriate choice below:
F) Body Type B (single-unit construction) ... 1.0
G) Body Type Z (multi-unit construction):
can be easily knocked out of alignment
when the utmost of care is not taken .... .0.75
If the binocular body is rubber-coated,
multiply the last result by 1.07.
IMPORTANT: A RUBBER COATING IS NO GUARANTEE THAT
A BINOCULAR IS WATERPROOF, NOR FOR THAT MATTER,
ANYTHING ELSE; A RUBBER COATING DOES HELP
PROTECT AGAINST SLIPPAGE AND IMPROVES HANDLING
WHILE BOATING OR AT SEA, HOWEVER.
I have taken the liberty to evaluate two binocular models. One is
Fujinon's 7X50, Model FMT-SX, a beautiful instrument for the money. The
other is the Minolta 10X50 Extra-Wide-Angle, Standard Model. Minolta once
sold Celtic binoculars, very well made second-source models, that appeared
nearly identical, as I recall, to models imported and distributed under
the Celestron name, circa late '70s.
FFQ = (OBJDSQR/100 x XSQR x RB x Q x FOVSQR x %FD x PRS x %LT x ER
-7
x OELD x FOC x C-F) x 10
Fujinon, 7X50, Model FMT-SX:
FFQ = (25 x 49 x 51.02 x 1.33 x 56.25 x 1 x 1.22 x 0.95 x 23
-7
x 27 x 1 x 1.45) x 10 = 487.97
Minolta, 10X50, Standard, Extra-Wide-Angle Model:
FFQ = (25 x 100 x 25 x 1.1 x 60.84 x 0.09 x 1.0 x 0.75 x 7.5
-7
x 18.75 x 0.75 x 0.863) x 10 = 2.57
It is remarkable that the FFQ ratio between the two models works out
to be approximately 190:1!
I trust that this tool will be useful for all those who are sincerely
interested in doing serious astronomy with binoculars.
25MAR90XMIT-DJB
David Jameison Brown
73257,3670/FRO