Effect of Magnification on Light Output from a Binocular (1 Viewer)

[grackle314]

Light coming out of a binocular exit pupil is related to the light going into the objective. Minus the transmission losses, the light power collected through the objective is concentrated into the smaller exit pupil. The exit pupil area is approximately equal to the objective area divided by the square of the magnification. For a fixed objective area, the light from a higher magnification will be more intense at the exit pupil, in watts per square millimeter since a higher magnification has a smaller exit pupil area.

As an example, a 42 mm diameter objective will have an exit pupil diameter of 4.2 mm for a 10x magnification and 5.25 mm exit pupil diameter for an 8x . The light power output is spread over the area of the exit pupil, which is reduced compared to the objective area by the square of the magnification. Hence, for a fixed objective the light intensity power per square mm at the exit pupil is higher for the 10x compared to the 8x by the ratio of the reduction of the areas: 100 / 64. Simply put, the light goes into a smaller area for the 10x than the 8x . Keep in mind that the human eye pupil also restricts the light entering the eye, frequently this eye restriction is much smaller than the exit pupil. In typical bright daylight, most human eyes have pupils of 2 mm diameter or less. The light arriving from the binocular exit pupil which is outside the eye pupil will not enter the eye, this light is wasted for observation except that a larger exit pupil makes it easier to find the image. For the fixed objective where exit pupils are greater than the eye pupil, the greater magnification will have greater intensity entering the eye approximately by the square of the magnification ratio. One would expect for a fixed objective area with exit pupil greater than the human eye that a 10x binocular compared to an 8x in daylight will deliver approximately 100/64 = 1.56 more light per square mm to the eye pupil.

Below are the results of an experiment done with binoculars I have at hand. There are two binoculars with 10x and two with 8x, representing four manufacturers and four sizes of objectives.

For a constant input flat sheet white light source at one meter from the objective with the objective looking down a 7.5 cm diameter 1 m long tube and using a Newport optical power meter model 840, the exit pupil power was measured and the exit pupil power per square millimeter calculated.

One may see in the chart below both 10x binoculars have exit pupil output power of 0.57 to 0.58 microwatts per square millimeter and the 8x binoculars are at 0.40 microwatts per square millimeter. The 10x deliver more light per square millimeter at the exit pupil than the 8x . To compare with the 100/64 expected ratio, 0.40 microwatts per square mm x 100/64 = 0.625 microwatts per square mm which is 8% above the observed 10x power per square millimeter. This is a simple experiment and gives average power density over the exit pupil. Refinements such as radial power profile would be expected to alter the results a bit. And the human eye perception of this power is not discussed here other than to note the human eye also has a radial power detection profile.

Binocular	M x Objective	Exit Pupil Diam.	Power out Exit Pupil (microwatts)	Microwatts per square mm
Swaro NL Pure	10x42	4.2	8.10	0.58
Zeiss VP	8x25	3.125	3.10	0.40
Kowa Genesis	10x22	2.2	2.17	0.57
Leica UVD	8x20	2.5	1.97	0.40

 

[Maljunulo]

Someone who knows what he is talking about needs to review this.

 

[John A Roberts]

Hi grackle314,

To help make things clearer for most including myself:
What are the implications of knowing about the light output of a binocular in microwatts?
And in what circumstances would it help in choosing between two binoculars?


John

 

[jring]

Hi,

the simple argument makes sense to me and the measured results match it - a physicists dream...
In this broad daylight scenario though, one of two things is going to happen in real life:

• the brain will be able to adapt to the different lighting conditions and make you perceive a perfectly lit image in both cases.
• the 10x image with its higher amount of energy in the eye pupil is a bit over what the brain can adapt for and thus the user perceives a better image in the 8x pair.

But the argument will also work for low light scenarios and larger exit pupils... imagine an elderly observer using 7x50 and 10x50 pairs in bad light. in this case the 7mm exit pupil of the 7x pair will be more than what his or her eye pupils can widen to. Once again the light not hitting the smaller pupil will be lost.
in case of the 10x50 the 5mm exit pupil will be inside (or close to that) the eye pupil and no or little light will not hit the eye pupil. In this case I would expect the user to have a better experience with with the 10x pair...

But measuring this scenario might be more tricky due to the sensitivity and error margin of the optical power meter...

Joachim

 

[Canip]

Light coming out of a binocular exit pupil is related to the light going into the objective. Minus the transmission losses, the light power collected through the objective is concentrated into the smaller exit pupil. The exit pupil area is approximately equal to the objective area divided by the square of the magnification. For a fixed objective area, the light from a higher magnification will be more intense at the exit pupil, in watts per square millimeter since a higher magnification has a smaller exit pupil area.

As an example, a 42 mm diameter objective will have an exit pupil diameter of 4.2 mm for a 10x magnification and 5.25 mm exit pupil diameter for an 8x . The light power output is spread over the area of the exit pupil, which is reduced compared to the objective area by the square of the magnification. Hence, for a fixed objective the light intensity power per square mm at the exit pupil is higher for the 10x compared to the 8x by the ratio of the reduction of the areas: 100 / 64. Simply put, the light goes into a smaller area for the 10x than the 8x . Keep in mind that the human eye pupil also restricts the light entering the eye, frequently this eye restriction is much smaller than the exit pupil. In typical bright daylight, most human eyes have pupils of 2 mm diameter or less. The light arriving from the binocular exit pupil which is outside the eye pupil will not enter the eye, this light is wasted for observation except that a larger exit pupil makes it easier to find the image. For the fixed objective where exit pupils are greater than the eye pupil, the greater magnification will have greater intensity entering the eye approximately by the square of the magnification ratio. One would expect for a fixed objective area with exit pupil greater than the human eye that a 10x binocular compared to an 8x in daylight will deliver approximately 100/64 = 1.56 more light per square mm to the eye pupil.

Below are the results of an experiment done with binoculars I have at hand. There are two binoculars with 10x and two with 8x, representing four manufacturers and four sizes of objectives.

For a constant input flat sheet white light source at one meter from the objective with the objective looking down a 7.5 cm diameter 1 m long tube and using a Newport optical power meter model 840, the exit pupil power was measured and the exit pupil power per square millimeter calculated.

One may see in the chart below both 10x binoculars have exit pupil output power of 0.57 to 0.58 microwatts per square millimeter and the 8x binoculars are at 0.40 microwatts per square millimeter. The 10x deliver more light per square millimeter at the exit pupil than the 8x . To compare with the 100/64 expected ratio, 0.40 microwatts per square mm x 100/64 = 0.625 microwatts per square mm which is 8% above the observed 10x power per square millimeter. This is a simple experiment and gives average power density over the exit pupil. Refinements such as radial power profile would be expected to alter the results a bit. And the human eye perception of this power is not discussed here other than to note the human eye also has a radial power detection profile.

Binocular	M x Objective	Exit Pupil Diam.	Power out Exit Pupil (microwatts)	Microwatts per square mm
Swaro NL Pure	10x42	4.2	8.10	0.58
Zeiss VP	8x25	3.125	3.10	0.40
Kowa Genesis	10x22	2.2	2.17	0.57
Leica UVD	8x20	2.5	1.97	0.40

This is interesting. Two questions:
What is the stated measuring precision of the 840?
When comparing two binos with same specs (e.g. 10x42), differences will show up due to different transmission etc, right?

 

[agus_m]

Is the experiment conducted in a pitch black environment? Is there a residual signal when the light is turned off? What is the precision of the instrument?

 

[Ignatius]

Very interesting.
Also, one question: how about same exit pupil size but different objective sizes?

 

[Tringa45]

By using a 7,5 cm dia. 1 m tube you are vignetting the objectives to a TFoV of 4,3°, so the measurements make no sense.
A telescope or binocular is merely a light funnel and the intensity of light at the exit pupil is that at the objective minus transmission losses and vignetting, but spread over a much greater angle.
Magnification is angular magnification, so the solid angle of the AFoV is approximately the TFoV multiplied by the square of the magnification.

John

 

[Ignatius]

By using a 7,5 cm dia. 1 m tube you are vignetting the objectives to a TFoV of 4,3°, so the measurements make no sense.
A telescope or binocular is merely a light funnel and the intensity of light at the exit pupil is that at the objective minus transmission losses and vignetting, but spread over a much greater angle.
Magnification is angular magnification, so the solid angle of the AFoV is approximately the TFoV multiplied by the square of the magnification.

John

Since this is about light entering the binoculars objective aperture from a homogeneus light source and not about looking through it at the world from the other end, I think vignetting and FOV reduction do not come into it. Like when the transmission of an optical system is measured - it matters only what goes in the front vs what comes out the back, not what looking into the back and out through the front shows of the world.

 

[Scott98]

microwatts?

 

[tenex]

If this argument were correct, one would be literally blinded using a telescope for daytime terrestrial viewing.

A binocular is limiting the light reaching the eye, not intensifying it.

The situation may be different in astronomy.

 

[Maljunulo]

The situation may be different in astronomy.

I don't see how it could be, and I'll go so far as to say "No, it isn't."

 

[grackle314]

Here are some answers to questions posed.

To John A Roberts:
The light level used in the experiment was in the microwatt level of detected power. This was shown to indicate the actual units of measure. For comparison to overhead summer sunlight which is about 1.4 kilowatts per square meter, a 1 microwatt per square millimeter is 1 watt per square meter, about 1,000 times less power per unit area than direct sunlight maximum.

The circumstances in which this knowledge would help in choosing between two binoculars would be to have basic understanding that higher magnification leads to higher light power per unit area leaving the exit pupil. This helps understand which exit pupil size is useful for light going into eye of known eye pupil diameter. For example, bigger objective for the same magnification may contribute a larger amount of light leaving the exit pupil but for which a larger fraction is not received within the eye. There is the complication of what the radial light power profile is at the exit pupil, the numbers above just give average power per unit area coming out of the exit pupils for the four binoculars tested.

To jring:
Yes, the brain perception plays a role not included in the measurements reported above.
Typically binoculars are used where 8x, 10x, 12x, and so on all are within what the brain can adapt for light levels. Humans detect light on roughly a logarithmic scale, a 50% increase is not particularly notable by most people. It is possible to see the difference with a human eye for sure when going up to 14x .
Yes, there is little to be gained purchasing a binocular with exit pupil far larger than your eye pupil maximum dilation. Given the range of human pupil diameters and the observing light levels, that is why there is a range of exit pupils available in binocular choices. I only buy binoculars that match my eye pupil and observing conditions, others will make different choices.

Yes, measuring the scenario of large versus small exit pupils would also benefit from radial light power density measurements, which I presently don't plan to undertake.

To Canip:
Measuring precision of the Newport Optical Power Meter Model 840 is about 5 nanowatts.
Yes, different transmission etc would provide differences in results between two binos with same specs (e.g. 10x42). However, for the four binos in the test, the transmission coefficients are pretty similar, maybe only a couple percent variation. I do have a Carson 12x32 which appears to me to have about a 60% transmission coefficient, hence not included in the comparison foursome.

To agus_m:
Yes, the experiment was done in a dark room. The residual signal detected was 16 nanowatts background. Given that level, I did not subtract background in the data analysis.

Precision of the optical meter is about 5 nanowatts.

To Ignatius:
Yes, that would be interesting to see same exit pupil with different objectives. I don't have that option at hand.

To Tringa45:
Yes, total field of view down the tube is about 4.3 degrees. Tube was used for secondary reduction of background light in dark room. The field of view for the tested binoculars was NL Pure 7.6 degrees, Zeiss VP 7.4, Kowa Genesis 6, and Leica UVD 6.47 . Yes, there is elimination of outer image light, but for images within the central half radius used for normal viewing the light was collected similarly to no tube being present. Also note the largest FOV and smallest FOV were for the 10x pair which yielded similar results and the 8x pair were similar to each other in result as well. This test was not a test of total light transmission, rather it is just one measure of average light power per unit area coming out of binoculars illuminated by the same light. Other test scenarios could well be undertaken by those interested in looking further into this question.

To Scott98:
Yes, microwatts was total power scale used for the detected light under the described illumination.

To tenex:
I don't know about telescope safety for blinding issues for daytime terrestrial viewing. One would need to find the power per unit area output and determine the eye safety threshold. Magnifying glasses can cause fires and binocular guidance always includes caution to avoid observing direct sunlight, which is dangerous to the eye even without binocular magnification. A binocular does intensify the light power per unit area coming out the exit pupil compared to the light power per unit area going into the objective.

 

[Maljunulo]

I still wish someone knowledgeable would step in here, if we haven’t scared them all away.

 

[Tringa45]

I still wish someone knowledgeable would step in here, if we haven’t scared them all away.

This is the largest collection of misconceptions I have ever seen on the forum and he obviously doesn't understand how a Keplerian telescope works.
If he is trying to tell us something, I don't know what it is.

 

[Binastro]

The damage to the eye using a telescope to directly view a bright Sun is instant.

My friend at age eleven put lenses from several sunglasses in front of a one inch telescope.
He had instant permanent eye damage for the rest of his life in one eye, but was a brilliant artist using his good eye.

With a binocular looking directly at the Sun you may be lucky enough to turn away quickly enough or blink.
Pupil response is too slow and anyway ineffective.
If the binocular is moving, then the Sun exposure may not be concentrated enough to do harm, but don't view the Sun with any optical instrument or the unaided eyes.

Papers from eye surgeons at the Royal Manchester Eye hospital indicate damage to the eye from exposures to the Sun of a few seconds with unaided eyes.
See Hazards of Light Pergamon Press.

See also papers by Dr Ralph Chou, Canada.

Also papers in the Journal of the Optical Society of America.

Medicines such as antibiotics increase the risk.

Some papers indicate eye damage at 1 to 11 seconds exposure.
Other papers up to 20 seconds.

US soldiers deliberately viewed the Sun for 30 seconds in their dominant eye to ensure they were returned home with permanent eye damage.

For faintest stars at night the results are linear with magnification not the square of the magnification. For the same objective aperture.

Regards,
B.

 

[Maljunulo]

This is the largest collection of misconceptions I have ever seen on the forum and he obviously doesn't understand how a Keplerian telescope works.
If he is trying to tell us something, I don't know what it is.

My concern has been addressed, and I am removing my comment.

 

[Brink]

It doesn’t make sense to concern yourself with the irradiance at the exit pupil, where if it is more concentrated it is also much more divergent. The light intensity on the retina is always the same (given an ideal 100% transmissive telescope). This would be true for your 7.5 cm circular object whether the binoculars are 8x, 10x, 12x, or through the unaided eye with no telescope at all. It is an immutable law of physics that you can never make anything brighter than it actually is with optics, the best you could ever hope for is to make the object almost as bright as it actually is.

It is certainly valid to point out that a large exit pupil has minimal benefit when the pupil is dilated smaller than it. This is a matter of opinion though, and there has been a lot of discussion about the pros and cons of larger than “necessary” objective binoculars.

 

[tenex]

To tenex:
I don't know about telescope safety for blinding issues for daytime terrestrial viewing.

Of course it's not an issue (as long as the sun is avoided). Compared to a binocular, even a spotting scope at 90x would be too bright for viewing comfort on your theory, as of course they aren't. Extreme cases often show the absurdity of misunderstandings, but you seem determined to ignore them.

Magnifying glasses can cause fires

Yes, I once enjoyed burning holes in things too, but binoculars (and telescopes) are afocal instruments that don't do that.

A binocular does intensify the light power per unit area coming out the exit pupil compared to the light power per unit area going into the objective.

This is irrelevant. One does not view an exit pupil.

 

[grackle314]

To Brink:
Absolutely correct, the etendue cannot be decreased in this situation. The higher power magnification will have more divergence in the smaller exit pupil. An exit pupil similar in size to the eye pupil will deliver a larger fraction of the collected light inside the eye compared to an exit pupil larger than the eye pupil. For a lot of binocular designs (say 8x42, 10x42, 12x42) increasing magnification increases the fraction of incoming light which may enter the eye because of decreasing exit pupil size with increasing magnification. No image will be "brighter" than the original object.