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Calculating image resolution (1 Viewer)

Omid

Omid

Well-known member
United States
Dear friends,

I am trying to make a calculation as to how much resolution (i.e. pixel/inch) we need in the image that the objective forms at the focal plane of the eyepiece. To make the question more clear, let us consider this similar problem:

We place an small LCD or OLED screen at the focal plane of a typical binocular eyepiece. Lets assume that this eyepiece has an apparent field of view of FOV=60 degrees, an eye relief of ER=20mm and effective focal length of f=15 mm. What is the minimum resolution needed for the screen so that a viewer can not see the individual pixels forming the image? We can assume that human eye has the ability to distinguish objects that are separated by 1 arc minute.

I appreciate any help as to how to best formulate the above calculation. B :)
 
Last edited:
. Hi,
I presume that you mean one arc minute?

There is also the interesting question of whether the Sony digital binoculars come anywhere near the resolution of optical binoculars.

I don't think at the moment even their second-generation DEV binoculars come close but I suppose we will get there in the end maybe in 7 to 10 years? Before optical binoculars are redundant.
 
Omid said:
Dear friends,

I am trying to make a calculation as to how much resolution (i.e. pixel/inch) we need in the image that the objective forms at the focal plane of the eyepiece. To make the question more clear, let us consider this similar problem:

We place an small LCD or OLED screen at the focal plane of a typical binocular eyepiece. Lets assume that this eyepiece has an apparent field of view of FOV=60 degrees, an eye relief of ER=20mm and effective focal length of f=15 mm. What is the minimum resolution needed for the screen so that a viewer can not see the individual pixels forming the image? We can assume that human eye has the ability to distinguish objects that are separated by 1 arc second.

I appreciate any help as to how to best formulate the above calculation. B :)
Click to expand...

The AFOV of 60 degrees means a maximum radial half-angle of 30 degrees, or 1800 arc minutes. The number of "pixels" of an area of 1 arc minute (squared) is then approximately 3.14*(1800)^2 = 10 MP, about 10 megapixel (perhaps 30 MP, if we need the same resolution for 3 colors). In reality, the resolution of binoculars is going down toward the edges, so that half of that would be sufficient (with pixels being coarser toward the edge).

The problem is not the sensor, in fact, but the monitor that is viewed through the ocular. Here, technology is currently stuck at 1 MP. Three generations (8-10 years) later and we should be there ...

Cheers,
Holger
 
To Binastro: Thanks for the feedbak, yes I meant 1 arc minute. I corrected the error in my original post.

OK, now lets do some analysis. Here I made a diagram to help visualize the problem better. If the field of view is 60 degrees and we need one pixel per each arc minute, then we need to fill the field of view with 3600 pixels along the diagonal. Now, how do we calculate the height of the image formed at the eyepeice focal plane? If we knew this length, then the LCD resolution would be 3600/(image height).

To Holger: I just saw your post. OK, so we need about 10 mega pixels in a circular area. This is in line with my calculation above. Now, what is the area of the image? In other words, what pixel density (line/mm or dpi) do we need?


Resolution_Analysis.jpg
 
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Hi Omid,
The focal length of an eyepiece is the effective distance from which your eye views the focal plane.

If the diameter of the focal plane equals the eyepiece focal length, the apparent field will be one radian. If you agree and understand, you can work it out from that. Eye relief does not enter into the calculation.

Ron
 
Omid said:
To Binastro: Thanks for the feedbak, yes I meant 1 arc minute. I corrected the error in my original post.

OK, now lets do some analysis. Here I made a diagram to help visualize the problem better. If the field of view is 60 degrees and we need one pixel per each arc minute, then we need to fill the field of view with 3600 pixels along the diagonal. Now, how do we calculate the height of the image formed at the eyepeice focal plane? If we knew this length, then the LCD resolution would be 3600/(image height).

To Holger: I just saw your post. OK, so we need about 10 mega pixels in a circular area. This is in line with my calculation above. Now, what is the area of the image? In other words, what pixel density (line/mm or dpi) do we need?


Resolution_Analysis.jpg
Click to expand...

The diameter of the real image can be calculated as follows:

Z = 2F tan(A/2)

where F is the focal length of the objective and A the true angle of view of the binocular. This at least defines the size of the sensor. The monitor could be of any dimension, of course, but one would probably choose something similar.

Apart from resolution issues, there is the computation issue: To have a nice view, you want a frame rate of 60 fps, and that with tens of megapixels. Consider how much power today's graphic engines are consuming. A direct mapping from sensor-pixel to monitor-pixel would certainly keep the computational costs far below those of a shooter game, yet this may not be an easy problem to solve.

Cheers,
Holger
 
ronh said:
Hi Omid,
The focal length of an eyepiece is the effective distance from which your eye views the focal plane.
Click to expand...

OK, then this means h=2f tan(AFOV/2) where AFOV is the apparent field of view, f is the eyepice focal length and h is the hight of the image at eyepiece focal plane (also the diameter of the field stop).

Holger's formula is clearly correct as the image formed by the objective will have a hight equal to h=2F tan (FOV/2).

So, for a binocular having 60 degress apparent field of view and f=20mm, we get h=23mm. This means the LCD needs 156 ln/mm or about 4000 dpi in resolution! This is way too high!! :eek!:
 
Last edited:
Omid said:
OK, then this means h=2f tan(AFOV/2) where AFOV is the apparent field of view, f is the eyepice focal length and h is the hight of the image at eyepiece focal plane (also the diameter of the field stop).

Holger's formula is clearly correct as the image formed by the objective will have a hight equal to h=2F tan (FOV/2).

So, for a binocular having 60 degress apparent field of view and f=20mm, we get h=23mm. This means the LCD needs 156 ln/mm or about 4000 dpi in resolution! This is way too high!! :eek!:
Click to expand...

Way too high in 2013 - let's talk again in 2020 :)

In any case, resolution (in terms of pixel counts) alone is not the main factor. Digital cameras began to dominate the market at a time when their resolution was far below that of film cameras. Since sensors nowadays have a higher resolution than monitors, digital binoculars make use of digital zoom and in this way increase their effective resolution. Then come additional image processing features: Note that the quoted resolution of the eye, 1 arc minute, is valid only at optimum contrast (test charts with black & white stripes). In real life, the resolution falls almost always below that optimum and remains limited by contrast and lack of light. The digital image can be boosted to perform better than the optical image and in this way show details which were invisible through an optical device.

So I predict: The digital binocular will become popular and powerful already with pixel counts far below 10 MP. They will first of all replace the night glasses and then begin to invade the mainstream binocular market.

Cheers,
Holger
 
Holger Merlitz said:
Way too high in 2013 - let's talk again in 2020 :)

In any case, resolution (in terms of pixel counts) alone is not the main factor. Digital cameras began to dominate the market at a time when their resolution was far below that of film cameras. Since sensors nowadays have a higher resolution than monitors, digital binoculars make use of digital zoom and in this way increase their effective resolution. Then come additional image processing features: Note that the quoted resolution of the eye, 1 arc minute, is valid only at optimum contrast (test charts with black & white stripes). In real life, the resolution falls almost always below that optimum and remains limited by contrast and lack of light. The digital image can be boosted to perform better than the optical image and in this way show details which were invisible through an optical device.

So I predict: The digital binocular will become popular and powerful already with pixel counts far below 10 MP. They will first of all replace the night glasses and then begin to invade the mainstream binocular market.

Cheers,
Holger
Click to expand...


On that final note:

“It is easy for me to imagine that the next great division of the world will be between people who wish to live as creatures and people who wish to live as machines.”

― Wendell Berry, Life is a Miracle: An Essay Against Modern Superstition (1999)

I think that Digital Binoculars are one of the things Wendell Berry was talking about.

Some people will be content with seeing only what the machine sees. So many of them are not content with seeing what their real eyes see!

Bob
 
I don't think the future's quite within sight yet. There's far more to it than just resolution. 3 colour displays RGB are quite rudimentary - already better displays are using 4 colours. 60Hz refresh rate is also pretty basic, 100, 200, or 400 is far more preferable. Then there's response time, and dynamic range, noise, moire, white balance and colour bit rates, etc to contend with ..... not to mention the computational brains to drive it all in real time ......

I have read of figures of 50MP, but it looks to be an area of active research. Apple is already claiming "Retina Displays" http://en.wikipedia.org/wiki/Retina_Display - forget the Samsung lawyers on the phone! - you boys give me a call sometime nearer to 2030 (with hindsight! - there is that minor little niggling problem of 'peak oil' to deal with after all ..... ) when you can offer some digital jiggerypoo that outdoes my MarkI analogue eyeball system and pea brain, for less than the price of an 2013 'alpha', and one that won't give me headaches, or leave me watching millions of unwanted little fireflys at night, long after the device has been switched off!


Chosun :gh:
 
Thank you very much everybody for your comments. Special thanks to Dr van Ginkel for posting his great article on human visual system and its connection to telescope and binocular optics. Very informative article!

I myself am not a great fan of electronic binoculars. I hunt and I am a big supporter of classical optical sights. If someone wants to watch wildlife on an LED screen, then they better stay home and watch Discovery Channel. I am ok with adding information to the natural image formed by a lens such as in a binocular with a laser range finder but don't like having a fully digital image.

My original reason for posting my question about resolution was my research on the design of a telescopic sight that uses a fiber optic connection between the objective part and the eyepiece part. I would like to transfer the objective image to eyepiece focal plane using a coherent fiber optic bundle. I wanted to know how much resolution is needed and how to calculate it. Based on our discussion, it seems that two key factors are

a) apparent field of view, each degree of AFOV needs to be covered by 60 pixels (or a bit less, may be 50 since 1 arc minute is the ideal resolution of human eye). This specifies total number of pixels needed.

b) the size of the image formed at the objective. By making this size bigger, we need less pixel density.

Is anyone familiar with fiber optic endoscopes? How much resolution do they have? :h?:
 
Echo the thanks to Gijs :t: - something I'll digest fully later - along with a cup of tea and some scones! :eat:

For now though, I'll mention, after too much time staring at this screen, that my dark adapted vision (and prolly daytime too, though perhaps less noticeable) is absolutely up the ess-haitch-1-tee !! When I close my eyes, it consists of a matrix of millions of little 'blinking fireflys' - red, yellow, green, blue. Very annoying.

The screen I am using is 15.6" diagonal (in a 4:3 aspect ratio), 1280 x 800 resolution (highest available) @ 60Hz, using 32-bit colours. Screen brightness is turned down to 60%, which is all the cruddy AR coatings will realistically allow for normal daytime, or lit-room use.

I can't imagine that even the better displays today of twice this res, or more, in a laptop screen, will get rid of the pesky 'fireflys' ......


Chosun :gh:
 
. It has to be borne in mind that the tables and graphs presented in the very informative article are generally average values.

For instance Iris size varies greatly between different individuals.
In my case my Iris is fully 50% larger than indicated in the graph, so the area of the pupil is more than double that stated.
I know some other individuals who have even larger irises or pupil sizes.

I found the graphs of resolution with handheld and tripod mounted or otherwise very steady binoculars very useful.
However, again this depends greatly on the individual and also on how long the individual is holding the binocular and whether the individual is tired or rested etc etc. and the shape, length and weight of the binocular.
But the graph is a good starting point.

Although my eyes have obviously less transmission than when younger I think they are not quite as deficient as the table mentions.
This may be because I am a regular solar observer and take very great care to minimise my exposure to sunlight. In fact I take vitamin D to maintain my correct level.
And England is often covered in cloud.

In addition some individuals have very much sharper eyes than others so that I think their central vision may contain closer elements in addition to having very good optics in their eyes.

But all in all it is a fine article, which combines all the main features in one place.
 
I have couple more generic question:

What are the typical objective focal distance and eyepiece focal distances for a 10X binocular?

What is a the typical focal length of a typical rifle scope objective? Is it reasonable to assume about 20 CM ??

Thanks!
Omid
 
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