Light throughput equation (1 Viewer)

[kimmik]

While twilight factor can guide you on how much twilight detail can be seen, I propose a light throughput equation, which allows you to compare the total photons passed through binoculars if used under the same environment. When your pupils are dilated, this factor correlates with the "wow so bright" feel. It doesn't correlate as well when your pupils are smaller than exit pupil.

Throughput = Aperture^2 x FOV^2 x transmission x vignette factor (where vignette factor is the size of exit pupil at the edge of eyepiece compared to center)

example - Noctivid 8x42: 42^2 x 7.7^2 x 0.9 x 0.5 = 47,000
vs - EL 8x32: 32^2 x 8^2 x 0.9 x 0.8 = 47,200

This does approximate my feel when using these two binoculars, which is that while they are in different aperture category, they are surprisingly comparable in global brightness sensation in dim conditions. There are other factors which also influence the sensation probably most notably blue spectrum transmission.

Another example - SLC 8x56: 56^2 x 7.6^2 x 0.93 x 0.7 = 118,000
NL 8x42 - 42^2 x 9.1^2 x 0.92 x 0.7 = 94,000

Under bright conditions (small eye pupils) on the other hand, the sensation of "wow so bright" has more to do with surface brightness, AFOV^2 x transmission.

 

[MiddleRiver]

hmmmmmm
this is interesting

 

[lilcrazy2]

While twilight factor can guide you on how much twilight detail can be seen, I propose a light throughput equation, which allows you to compare the total photons passed through binoculars if used under the same environment. When your pupils are dilated, this factor correlates with the "wow so bright" feel. It doesn't correlate as well when your pupils are smaller than exit pupil.

Throughput = Aperture^2 x FOV^2 x transmission x vignette factor (where vignette factor is the size of pupil at the edge of eyepiece compared to center)

Can you explain how you arrived at the vignette factor? You lost me there.
thanx

 

[kimmik]

Can you explain how you arrived at the vignette factor? You lost me there.
thanx

Looking at the exit pupil, you’ll find it doesn’t stay the same round shape across the entire field of view.

This is the vignette, darkening of the image periphery.

It would be too difficult to map the vignette precisely to find the light loss, so my approximation is to imagine the phases of the moon, eg waxing gibbous moon would be around 0.75.

Lunar phase - Wikipedia

en.m.wikipedia.org

 

[Maljunulo]

I am confused by post #4.

One does not customarily look through a binocular from a significantly off-axis position, hence I don‘t follow your illustration of the exit pupil “not staying the same round shape”.

Can you educate me?

 

[kimmik]

though your eye is not pointed sideways, the peripheral image light originated from that angle. Wide AFOV and all.

These ray diagrams may make the concept clearer.

Ray Optics Simulation of Swarovski NL, SLW

To help me understand the optical design of the NL series, I have approximated the design using the online simulator linked below. The design file is attached so you may do your own modifications, including changes to the field flattener lenses, to see its effect on field curvature, field of...

www.birdforum.net

 

[henry link]

There are some methods for making more precise images of off-axis vignetting in different binoculars.

One is to shine a laser pointer into the objective lens with the laser output covered by a piece of frosted tape. The three photos below show (left photo) the shape of the on-axis exit pupil projected by the Swarovski 8x42 NL onto a white surface placed about 50mm behind the eyepiece. It's actually a prefect circle, but looks oval because it had to be photographed from the side. The middle photo shows the change in shape of the off-axis exit pupil caused by vignetting when the laser pointer is moved to a point about 2/3 of the distance to the objective lens edge and the right photo shows the off-axis exit pupil as it appears when the laser is moved almost to the edge of the objective lens.

I also use a purely visual method that I can't photograph. It involves stretching a piece of aluminum foil over the objective and punching a pinhole in the foil (photo on the extreme right). What you see when you look through the binocular is the part of the FOV that is fully illuminated by light entering the objective lens at the position of the pinhole.

By moving the pinhole around and measuring its distance from the center (or edge) it's possible to find the size of the clear circle at the center of the objective lens that fully illuminates the entire FOV. The dirty little secret is that circle is not very large in any binocular, because it would require impractically enormous prisms. In the 8x42 NL the completely clear un-vignetted aperture is a little less than 10mm. Outside that circle the shape of the exit pupil gradually shrinks toward a narrowing cat's eye shape. The size of the clear aperture, the slope of its shrinkage and it's final shape and size at the field edge are affected by many things, including the exit pupil size, the prism size, the the diameter of the eyepiece fieldstop and the baffling design including the size of the baffles and where they are placed.

 

[tenex]

The dirty little secret is that circle is not very large in any binocular

So essentially, there's so much gradual vignetting that one doesn't notice it, as in photographs with visibly darker edges around a mostly fully illuminated area.

 

[henry link]

Exactly. The eye doesn't notice very gradual dimming and, of course sometimes there isn't any dimming in daylight conditions when a very large exit pupil is combined with a very small eye pupil. A shrunken 7mm exit pupil near the field edge may still have a cat's eye shape with a minor axis of 3mm, so possibly still larger than the eye's pupil.

 

[Binastro]

The problem with a non full moon is that the albedo drops rapidly.

The albedo of a full moon is about 0.12.
The albedo of a half moon is 0.02.

The brightness of a half moon is very much less than half a full moon.

I don't know if the surface brightness of vignetted binocular images is constant or not.

Regards,
B.

 

[kimmik]

B, no dimming to that degree for surface brightness - slight colour shift and maybe minor dimming in the region of 10 percent in the EL is my estimate.

The cats eye vignette has one benefit, it reduces kidney bean as shown in my other thread on blackout. Long eye-relief eyepieces especially will benefit, that includes NL and Noctivid.

The presence of vignette is why larger exit pupil is in practice brighter, even during daylight - the periphery is always smaller than spec.

 

[kimmik]

A couple more examples, which are consistent with my observation:

Ultravid 8x20 - 20^2 x 6.5^2 x 0.92 x 0.7 = 10900

Curio 7x21 - 21^2 x 7.7^2 x 0.92 x 0.7 = 16800

Zeiss VP 8x25 - 25^2 x 7.4^2 x 0.92 x 0.7 = 22000

Since these are small exit pupil binoculars, the brightness difference is observable at all times other than under bright sunlight.

 

[kimmik]

Since we now know the light throughput, we can do a throughput per mass metric:

Zeiss FL 7x42 - 84000/740 = 113
NL 8x42 - 94000/850 = 110
SFL 8x40 - 64000/640 = 100
SLC 8x56 - 118000/1250 = 94
SF 8x42 - 72000/780 = 92
SF 8x32 - 50000/600 = 83
EL 8x32 - 47200/600 = 78
Zeiss VP 8x25 - 22000/290 = 76
Nikon WX 7x50 - 170000/2500 = 68
Curio 7x21 - 16800/250 = 67
Noctivid 8x42 - 47000/850 = 55
Ultravid 8x32 - 28000/540 = 52
Ultravid 8x20 - 10900/230 = 47

Now a pattern emerges, which explains at least in part, why the Zeiss VP 8x25 is said to have a big-bino feel. It has excellent throughput per mass, best of the pocket binos.

Leica's approach it would seem consistent, is high contrast but lower throughput.

A few 10x examples assuming vignette factor 0.7:

NL 10x42 - 65600/860 = 76
SFL 10x40 - 44000/640 = 69
SF 10x42 - 48000/780 = 62
SF 10x32 - 36300/590 = 62
NL 10x32 - 36300/660 = 55

 

[tenex]

I suspect that typical Porro designs have more generous prisms (with less vignetting) and this is part of their charm, or would still be if more were made today. Do Abbé-Königs do better than Schmidt-Pechans?

 

[kimmik]

I don't have enough porros to make any generalisations, but the Habicht has fairly low vignetting. Will look up some ak models later and add here.

Habicht 8x30 - 75
Habicht 10x40 - 67

The larger habicht is quite good for a 10x, nearly SFL level.

Conquest HD 10x56 - 66
SLC 10x56 - 67
FL 10x42 - 49

SLC 10x42 - 57
SLC 8x42 - 85

So not all AK prism models make it to the top of list like FL 7x42.

 

[kimmik]

Exactly. The eye doesn't notice very gradual dimming and, of course sometimes there isn't any dimming in daylight conditions when a very large exit pupil is combined with a very small eye pupil. A shrunken 7mm exit pupil near the field edge may still have a cat's eye shape with a minor axis of 3mm, so possibly still larger than the eye's pupil.

Would you have any thoughts about the amount of vignetting for 8x vs 10x versions of each model? I haven't paid enough attention to 10x, but wonder if there is less vignetting in the 10x versions, or if the baffle adjusted to achieve the same degree of cats eye at the periphery.

 

[henry link]

I think everything about vignetting would remain the same in simple 8x32/10x40 binoculars if the same eyepiece and prism housings were combined with objective lenses of the same focal ratio, but I don't think there are very many examples of that in the real world. The 8x30 and 10x40 Habichts, for instance, share the same eyepiece and prism housings, but the objective lenses of the 10x40 have a lower focal ratio than the 8x30. That leads to a smaller area of apparent field that is completely free of vignetting in the 10x40, but also a shallower slope of vignetting in the outer part of its apparent field.

The Nikon 10x35/8x30 EII also use the same eyepiece and prism housing, but show the opposite vignetting behavIor. The 10x35 objective has a higher focal ratio than the 8x30 objective, so it's vignette free area is larger than the 8x30, but the 10x35 has a steeper slope of vignetting in the outer part of the field.

In modern binoculars the focal ratio of the objective lenses, the strength (positive or negative) of the focusing lenses, the focal length of the eyepieces and the diameter of the eyepiece field stops may all change between 8x30/32 and 10x40/42, so I don't think a prediction of vignetting differences between 10x and 8x is possible based on magnification alone

 

[kimmik]

I quite like binoculars that have fixed prism and eyepiece, and change magnification purely through objective lens swap.

E.g. in addition to your mentioned habicht and E2, also the leica 8x20 and 10x25.

They make a lot of sense in that:
1. the 10x has a longer body helping with stability
2. the exit pupil stays the same size
3. they use the entire prism aperture, unlike fixed bodyshape models, that crop off the outer image circle
4. because of 3, they seem to have better light throughput per weight, as you're not carrying unused prism.
5. the cost savings of not having to develop multiple versions of eyepiece

 

[elkcub]

Since we now know the light throughput, we can do a throughput per mass metric:

Just to be clear, are you referring to the weight of the binoculars, and if so in what units?

Ed

 

[kimmik]

Just to be clear, are you referring to the weight of the binoculars, and if so in what units?

Ed

Exactly . Light throughput vs Weight.

I have in mind a graph which will be done when there is some free time, like holger’s AFOV vs k distortion.

There will be very interesting patterns emerging.

Units are arbitrary as we are comparing, just need to use the same units between comparisons.

I have used degrees, grams, millimeters.