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