Need help with viewfinder calculations

[pete_s.]

<p>Earlier posts about mirrorless FX cameras made me think about the viewfinder.</p>

<p>I would like to calculate how many pixels you would need in an electronic viewfinder for it to be the same size and apparent resolution as the viewfinder in a D800, assuming 20/20 vision.</p>

<p>There are viewfinder magnification, resolution limits of the eye, projection distance and size of the virtual image in the viewfinder and whatnot. I just seem unable to wrap my head around it.</p>

<p>Anyone know how to calculate this?</p>

<p>J<em>ust as a comparison my GH3 has 1.34x viewfinder magnification (m43 camera so equivalent to 0.67x on FX) and 16:9 format with 1.7 million dot equivalent OLED panel.</em><br>

<em> </em><br>

<em>Viewfinder magnification on D800 is approx 0.7x according to the user's manual. Since the focusing screen is "ground" I don't know how that fine pattern on the focusing screen affects it's apparent resolution in real life or how to calculate the size of the "grain" if possible. Unless someone has a better idea perhaps it's best to assume an "ideal" focusing screen and let the eye be the limit of resolution.</em><br>

<em> </em></p>

 

[rodeo_joe1]

<p>There's no point in having resolution greater than that of the human eye, so this should be the absolute limit of what's needed.</p>

<p>Looking at some figures for maximum cone density (on average a linear density in the region of 500 per millimetre) and dividing by the image focal length of the eye (~ 23mm) we get an angular acuity of 0.005 degrees. How this translates to pixels/mm depends on the angle subtended by the viewing screen to the eye.</p>

<p>I'd say that a HOV of 45 degrees would be a pretty good field of view for a viewfinder. This gives a figure of 9,000 pixels x 6,000 for the full-frame 3:2 aspect ratio = 54 megapixels. However, having done the maths, that looks like complete overkill to me, and I'd be surprised if half that resolution wasn't nearer to what was practically useful. The pixel grid just needs to be below what's discernible as "dotty" to the eye.</p>

[Ed_Ingold]

<p>The answer is highly subjective, but I'll give it a try. If full-sized is defined as an 8x10" print held at 16" from your eye (reading distance), and you can't discern anything better than 300 dpi at that distance, then you would need about 2 MP in the finder. Multiply that by the magnification (e.g., .7) and 1.4 MP would suffice. I know that the 2.3 MP, 0.78x finder in my Sony A7Rii is finer than my eye can resolve.</p>

<p>Another question is whether the lag and update time is discernible to the eye. The A7Rii finder updates (estimated*) 60 fps, which is well under the retention time in your eye of about 24 fps. The lag time of an optical finder is zero, but that of the A7Rii finder is small enough that I have no difficulty capturing the peak of action. The shutter lag is the limiting factor, and is comparable to that of a D3, or about 30 msec (estimated). Putting this another way, I have no means of objectively measuring these times, but the response time does not inhibit my ability to capture action.</p>

<p>Unlike the ground glass of an SLR, which is relatively transparent, the focal plane of an EVF is clearly defined. It is much more accurate to manually focus a lens on an EVF than a GG, and focusing aids such as magnification and peaking give an additional 5x to 12x advantage over the SLR. In essence, every shot uses live view. Auto focus does not depend on the viewfinder for either an SLR nor an EVF, but is approximately the same or faster on my A7Rii than on my D3, even in low light (< 5 lumins).</p>

<p>* One basis for my estimate is the tip of a (classical) conductor's baton, which peaks at about 30 mph. The apparent motion in the finder between updates is comparable to a shutter speed of 1/60.</p>

[pete_s.]

<p>Rodeo Joe,<br>

That seems way to much to me too. But I think we are getting somewhere here.</p>

<p>What about the horizontal field of view for the viewfinder? If the magnification of the viewfinder is 0.7x wouldn't HOV translate into HOV of 50 / 0.7 = 71.4mm lens? Or do should we do 0.7 x the HOV of a 50mm lens?</p>

<ul>

<li>Option 1: HOV of a 71.4mm lens is 28.3 degrees according to online calculators.</li>

<li>Option 2: HOV of a 50mm lens on full frame is 39.6 degrees so the HOV of the viewfinder should be around 0.7x39.6 = 27.7 degrees.</li>

</ul>

<p>Looking at some numbers I found that: <a href="https://www.nde-ed.org/EducationResources/CommunityCollege/PenetrantTest/Introduction/visualacuity.htm">"The standard definition of normal visual acuity (20/20 vision) is the ability to resolve a spatial pattern separated by a visual angle of one minute of arc."</a> I remember having seen this definition before when calculating DoF dependent on visual acuity and also the 8x10" print @ 300 dpi at 1 foot distance.</p>

<p>Anyway, one minute of arc is 1/60th of a degree. So 27.7 x 60 = 1662 pixels. For a 3:2 aspect ratio that's 1662 x 1108 pixels, or 1.8 Megapixels.</p>

<p>Since camera manufacturers seems to like to have big numbers for their displays they say dots and you need 3 dots (RGB) to form a pixel so 1.8 x 3 = 5.4 million dot EVF.</p>

<p>Sony A7R2 has 2,359,296 dots in their EVF. About the same as Panasonic in their GH4. <br>

That's 0.786 megapixels. I don't think they are 3:2 aspect ratio but if we assume that we get 1086 x 724 pixels. Hmm, that's very close to the 1024x768 4:3 standard. Either way it about 65% of the maximum resolution need (if calculations above are correct). About equivalent to a 200 dpi print instead of a 300 dpi.</p>

<p> </p>

[pete_s.]

<p>Very interesting post Edward. I didn't see it until after I wrote the reply above.</p>

<p>I have a GH3 and I can't really discern the pixels in that either. However I remember reading somewhere that OLED EVF doesn't have the same space between pixles (or dots) as for instance computer screens.</p>

[pete_s.]

<p>Interesting to note is that the LCD on the D810 has 1,229,000 Dots.</p>

<p>That means that the EVF of cameras like GH3,GH4,A7R2 (and probably most other newer mirrorless cameras) have more pixels in the viewfinder than there is on the back of the LCD on the best DSLRs.</p>

 

[rodeo_joe1]

<p>Pete: The focal length of lens fitted has no bearing on viewfinder angle-of-view. It's the angle subtended to the eye by the viewing screen that counts, whether a lens is attached to the camera or not. My 45 degrees horizontal AOV was just an estimate, and in any case would vary with eye relief and maybe with an individual's eyesight and any dioptric correction needed.</p>

<p>The maximum cone-density thing may well be a red herring, but reliable information about human visual acuity seems to be one area where the internet has very little to offer. The anatomy of the eye seemed like a good place to start, rather than the oft-quoted 300dpi at 12", which doesn't appear to be backed up by any hard evidence.</p>

<p>However, let's take those rule-of-thumb figures. That would give us an acuity angle of 0.016 degrees and (assuming my guess of 45 degrees HAOV is about right) a pixel number of just over 2800. Now 2700 * 1800 pixels seems much more realistic to me, giving a 5 megapixel EVF.</p>

<p>Having said that, I can see a distinct difference in a 10" x 8" print between a 5 megapixel and 12 megapixel camera image at normal viewing distance. More hard data needed I think! Especially the 1 minute of arc figure you quoted needs clarification. Because to actually resolve detail <em>within</em> 1 minute of arc would need a visual acuity of twice that figure. However if it means detail literally separated by 1 minute of arc, then the above working stands.</p>

<p>PS: If I get the time I'll stick an old F2 focusing screen under a microscope and get some idea of what the etch size is like.</p>

[Ed_Ingold]

<p>The rear screen on the D800 serves as the live view monitor. The rear screen works that way on the Sony A7 too, with a similar resolution, 1.2 MP. The Sony EVF has much higher resolution at 2.36 MP, but no optical finder. Sony has a different design philosophy which emphasizes the EVF for eye level use, in a compact, rugged magnesium housing resembling the prism on a DSLR. The rear screen is better suited for menus and viewing images, but these function are duplicated in the eyepiece as well.</p>

<p>Auto focus DSLR finders are designed to give you a bright, clear view of the subject, which works against precision manual focusing. Your eye tends to focus beyond the ground glass itself on a virtual image. Your eye itself seeks its sharpest focus, which may not be that of the sensor. The trick is to focus on something in the screen, like grid marks, then focus the lens so that the image and grid marks are in focus at the same time. That comes easily with a little practice.</p>

<p>SLR lenses usually remain wide open until the moment of exposure. Thus the DOF is at a minimum, making the focal point easier to discern. Lenses on a mirrorless camera behave differently. In many cases, the lens immediately stops down to where you set it. The viewfinder automatically brightens to maintain a reasonably constant level. It's like using the DOF button on a DSLR, but without a darkened screen.</p>

<p>Auto focusing is much quicker with an open aperture, and necessary if phase detection is used. This is SOP for DSLR cameras, but a Sony auto focus lenses must be "fooled" into keeping the aperture open. It defaults, as it were, to DOF preview. What fun it is to puzzle these things out.</p>

[bebu_lamar]

<p>The resolution only needs to be high enough to manually focus easily (without using the magnifying or focus peaking). For that about 2 to 4 MP is enough.</p>

[wayne_f1]

<p>I'm not sure the question is answerable, one is analog and one is digital, but we do see the rear LCD larger than the viewfinder. My notion is we see the viewfinder more clear, with more detail.</p>

<p>The D800 viewfinder is showing a 36x24mm image area, at 0.7x magnification (smaller). So that must compute about 1.0 x 0.67 inch size. But it is an analog image. It is high resolution, lens resolution, lots and lots more than we can see. The sensor calls it 7360x4912 pixels, and we are just barely daring to remove the anti-aliasing filter (D810), which can only be called the Minimum sampling resolution. (AA filters have always been used because our sensors did not have the minimum 2x sampling resolution to prevent false aliasing we call moire).</p>

<p>The LCD is about 2.5x1.87 inches. It shows 640x480 pixels (which x3 for the RGB components, is the 921K dots). So that is about 640 pixels / 2.5 inches = 256 dpi resolution, which is good, near the 300 dpi the eye is said to be able to see (at let's say the same close viewing distance).</p>

<p>They don't seem that dissimilar of size, but the viewing distances are different. So we do see the LCD larger, and at fair resolution, but not quite as good as the analog image the lens projects (which is the analog lens image, no sampling). My own notion is we can see better detail in the viewfinder (until we zoom the rear LCD view).</p>

<p>So to match the viewfinder lens image, we would need more pixels in the LCD than we have... But it would still be digitally sampled, and as such, 2x sampling resolution is the Minimum required to reproduce it without aliasing (moire). And that's minimum, greater oversampling would be a better image.</p>

<p> </p>

[Ed_Ingold]

<p>In the absence of noticeable lag, you really don't notice that the viewfinder is electronic rather than optical. You soon appreciate that the finder is nearly as bright in dim light as in daylight - brighter than to the naked eye. In extremely dim light, you see more noise as the gain increases, but not to unuseable levels. The finder is merely a window on the sensor itself, so the granularity is well below resolution levels until magnification is applied. Small, rapidly moving things like drumsticks or a conductor's baton show a stroboscopic effect, which is somewhat distracting. (For video, I increase the shutter angle to avoid a strobe effect, which is annoying if persistent.)</p>

[pete_s.]

<blockquote>

<p>Pete: The focal length of lens fitted has no bearing on viewfinder angle-of-view. It's the angle subtended to the eye by the viewing screen that counts, whether a lens is attached to the camera or not. My 45 degrees horizontal AOV was just an estimate, and in any case would vary with eye relief and maybe with an individual's eyesight and any dioptric correction needed.</p>

</blockquote>

<p>Rodeo Joe, I agree with what you are saying but I think you might be wrong about the viewfinder angle. Since we are viewing a virtual image from the focusing screen it's has certain size at a certain focusing distance. That means it has a certain field of view. As you said, this doesn't change regardless of the focal length. But what is that angle?</p>

<p>Well, the camera manufacturer uses the 50mm focal length to give as us a magnification value (at a certain diopter setting). That is an indirect measure of field of view, don't you agree? A large magnification means a large image in the viewfinder (and a larger field of view) and a small magnification a smaller image and a smaller field of view.</p>

<p>If the viewfinder was 1x magnification the image in the viewfinder has to be the same angle of view as a 50mm lens - since the magnification is only 1x at 50mm. Think about it. This is how Nikon tells the angle of view of the viewfinder.</p>

<p>That field of view stays the same regardless of what lens we put on. When the viewfinder magnification is 1x we can look through the lens with one eye and at reality with the other and our brains will blend it into one perfect picture.</p>

<p>Sure if we use glasses or take our eye further away from the viewfinder or adjusts the diopter the size changes a little but I bet that there is a CIPA or ISO standard that defines exactly how and where the magnification is measured. Regardless of that, I think we can disregard this effect is it doesn't cause any significant changes and should be the same for the same person regardless of camera.</p>

<p> </p>

[pete_s.]

<blockquote>

<p>The D800 viewfinder is showing a 36x24mm image area, at 0.7x magnification (smaller). So that must compute about 1.0 x 0.67 inch size. But it is an analog image. It is high resolution, lens resolution, lots and lots more than we can see.</p>

</blockquote>

<p>Wayne, it is an analog image (kind of) but even if we have unlimited resolution of that image, our eyes couldn't see it because they have limited resolution.</p>

<p>There is also the problem that the viewfinder image is a virtual image of the focusing screen. The lens projects the image onto the focusing screen through the viewfinder. And we look at a virtual image of the focusing screen. If you look closely you'll see that the virtual image appears to be about 3 feet (I'm guessing here) away from the camera while in reality it is just a one or two inches away.</p>

<p>The focusing screen itself is simplified a diffuse piece of plastic but it's actually a pattern of very small cones or pyramids on it. That's why Rodeo Joe said he would stick one of his screen under a microscope to see how these look and how close they are.</p>

<p> </p>

[kivivuori]

<p>The highest resolution EVF to date has 1280 x 960 pixels RGB = 3,68 MP. Aspect ratio: 4:3. I believe that the physical size of that sensor in actually very small ( < 0,5").<br /><br />It is truly excellent but ocular should be larger for the people like me who use glasses. The best optical viewfinders have still an edge compared to EVF:s.<br /><br />It´s not a question about resolution or refresh rate, but more like the construction and size of the ocular and high eye-point (which makes the physical size of the viewfinder larger).<br /><br />BR<br /><br /><br />Esa Kivivuori<br />Finland</p>

[kivivuori]

<p><br /> <strong>Sony A7 RII EVF specifications:</strong><br /> EVF: 1.3cm (0.5-inch) 2.4M-dot XGA color OLED,<br /> 100% coverage, 0.78x magnification, -4.0 to +3.0 diopter,<br /> Eyepoint 23mm from the eyepiece lens/18.5mm from the eyepiece frame at -1 m-1<br /> (CIPA standard), eye sensor<br /><br />Note:<br />2,359,296 dots (786,432 pixels)<br /><br /><br />BR<br /><br />Esa</p>

<p> </p>

[Ed_Ingold]

<blockquote>

<p>If the viewfinder was 1x magnification the image in the viewfinder has to be the same angle of view as a 50mm lens</p>

</blockquote>

<p>The traditional "normal" field of view has a corner-to-corner angle of approximately 45 degrees, which corresponds to that of a 50 mm lens (approximately), about the same as an 8"x10" print held 16" from your eye (reading distance). It's actually too much to take in at once without scanning, so a 70% or so magnification is probably more practical in a viewfinder.</p>

<p>A perfectly "ocular" finder is probably best represented in a rangefinder camera. The magnification of my Leica M9 is 91%, but perfectly usable. The 50mm frame occupies most but not all of the field, and 90mm and 135mm less yet. The 50mm frame is a bit of a stretch while wearing glasses. The M3 is nice for viewing, but it's much easier to focus with the A7.</p>

<p>Although the eyepoint of the A7Rii (and A7ii) is substantial, I find it hard to see then entire field while wearing glasses. A little "scanning" is required.</p>

[bebu_lamar]

<p>Given that the D810/D800 has a viewfinder magnification of 0.70x and Nikon generally put the apparent distance at 1m. So you have an image in the viewfinder that measured roughly 319mm x 479mm at a distance of 1m from your eye. <br>

So what's an EVF has to do Peter S?</p>

[kivivuori]

<p><strong>Leica M9</strong> viewfinder magnification is 0.68x (not 0,91x).</p>

[Ed_Ingold]

<p>I meant to use an M3 as an example. The M9 has a 28 mm frame which comes nearly to the edges. The 50 mm frame occupies only half of the finder window. I'm not sure I could hold the M9 up as a shining example of a good viewfinder.</p>

[rodeo_joe1]

<blockquote>

<p>"....But it is an analog image. It is high resolution, lens resolution, lots and lots more than we can see."</p>

</blockquote>

<p>Not so on either count. Try looking at a scene with lots of fine detail directly with the eye and then through the D800 (for example) viewfinder. You just won't be able to see the same amount of detail through the camera unless you use a medium telephoto lens (>105mm IME).</p>

<p>Also a DSLR screen has a reticulated finish - like fine crazy paving - that splits the image up into small irregular areas. It's not analogue in the true sense of the word at all. The "crazy paving" is very fine, averaging 5 microns square or so as seen through a microscope, but it's finite and puts a limit on viewable detail.</p>

<p>Edit: Pete, you really have to let go of the idea that the taking lens has anything to do with viewfinder resolution. I'll repeat that it's the angle that the eye sees the viewing screen as having that's necessary to know, and this doesn't change when you put different lenses on the camera.</p>

<p>It's true that viewfinder "magnification" is usually quoted with a "normal" lens (~50mm for full frame), but that's totally irrelevant when talking about the viewing screen itself. If we really saw the screen at 0.7x magnification it would appear to be only 25.2 x 16.8mm in size, and that's plainly completely wrong. The angle that the focussing screen subtends to the eye is what's needed as a starting point for calculating the resolution number you're after. This can be measured for your personal eyesight and eyepoint by setting two points <em> outside of the camera</em>, that are in line with the limits of the screen. Then you can measure the angle between those lines or points to where your eye was at the camera finder. It's pretty simple but just time-consuming.</p>

[rodeo_joe1]

<p>OK. I've just peered through my D800 viewfinder and pulled the camera back until the width of the viewfinder screen appeared the same width as my laptop screen. The laptop screen is 13.5" across and the distance need was approximately 27" - although it's not easy to judge exactly I'll admit. Tip: If you're going to try this yourself it's a lot easier if your take the lens off the camera.</p>

<p>Anyhow, that makes the subtended viewfinder angle around 28 degrees. Quite a bit narrower than what I'd estimated before, and that makes the number of pixels needed a lot fewer. (28 degrees divided by the accepted eye acuity angle of 0.016 degrees is 1750.)</p>

<p>I've also taken a photomicrograph of the texture of an old F3 screen - see below. It's from the fine-ground area around the split-image of a K type screen taken with a 100x objective. I measured the "features" with a calibrated PTI measuring eyepiece and they vary between ~2 microns to ~10 microns. An average of 5 or 6 microns square would be about right, but you can see how random and irregular the surface is. If they were a regular 5 microns each, there would be 7200 of them across the width of the screen, and half this number would be the limit of resolution of the viewfinder in lppmm. However I'm extremely doubtful that anyone's eyesight is good enough to see that amount of detail.</p><div></div>

[pete_s.]

<p><strong>FOCUSING SCREEN LIMITATIONS</strong><br /> Thanks Rodeo Joe, that's a very interesting photograph. The irregularities are smaller than I would have expected.</p>

<p>In Nikon's patent below it says that older technology focusing screens (before 1985, like the Nikon F3) the pattern was made by sandblasting. This newer patent is for another technique and the size of the features on the screen are 8.5 to 52.8 μm. The features on the focusing screen form a micro array of lenses.<br /> http://www.freepatentsonline.com/4519686.pdf</p>

<p>Having looked over a bunch of other newer patents from Nikon, Canon, Olympus etc it seems like an average of 20-30 μm pitch of microlenses are common. That's larger than the F3 you measured but probably more descriptive of current generation brightness optimized focusing screens like in the D800.<br /> 20-30 μm is 1200 to 1800 microlenses across the width of the focusing screen. That's the same as 0.96 to 2.2 Megapixels if it was an EVF.</p>

<p>...<br /> <br /> <strong>VIEWFINDER FIELD OF VIEW</strong><br /> Regarding the HOV of the viewfinder, 28 degrees, that's exactly what I calculated from the magnification and angle of view of a 50mm lens. Thinking more about it I have come to the conclusion that to get the field of view I should use my option 1 in an earlier post.<br /> So the complete formula to get the horizontal field of view in the viewfinder becomes:</p>

<ul>

<li>Full frame: HOV = 2*arctan(0.36*M*fc)</li>

<li>DX: HOV = 2*arctan(0.24*M*fc)</li>

</ul>

<p>HOV is the horizontal field of view. M is the magnification of the viewfinder, fc is frame coverage (1=100%).<br /> So for the D800/D810, 100% frame coverage, 0.7x magnification. Viewfinder horizontal angle of view = 28 degrees.<br /> For the D7200, 100% frame coverage, 0.94x magnification. Viewfinder horizontal angle of view = 25 degrees.<br /> For the Nikon FM3, 93%frame coverage, 0.83x magnification.Viewfinder horizontal angle of view = 31 degrees.</p>

<p>As you mentioned Joe, 28 degrees divided by the accepted eye acuity angle of 0.016 degrees is 1750. So the visual limits of a viewfinder equal in size to the D800 is about 2.0 Megapixels.<br /> ...</p>

<p><strong>IN SUMMARY</strong><br /> So in summary, viewfinders in size similar to D800:</p>

<ul>

<li>Visual limitation: about 2.0 Megapixels</li>

<li>Optical viewfinder focusing screen limitation: 1.0 to 2.2 Megapixels</li>

<li>Current EVF technology: 0.8 Megapixels.</li>

</ul>

<p>Also, big thanks to everyone who posted in this thread! I've read every post in depth and thought about what you have written. There are many caveats to calculate thing like this but I think this is as close as it is going to get.</p>

<p> </p>

[rodeo_joe1]

<p>Interesting that the patent application you linked to gives such a large-sized granularity Pete. Of course the patent application and practical implementation might be completely different, since it's the manufacturing process that's being patented. I'm not going to prise the screen out of my D700 or D800 to find out thanks!</p>

<p>I used the F3 screen because it was an old and scratched one that I had lying around. Visually it doesn't look that much different from a modern DSLR screen, apart from the split-image circle. I also think that the F3 screen is not strictly a "blasted" surface, but a moulded synthetic one. The photomicrograph I posted obviously only shows the 2D outline of its topology, but when I change focus through the microscope I can see that the features are like rounded hillocks of varying height. In other words they're irregularly shaped micro-lenses.</p>

<p>Anyhow, I think we finally agree that an EVF around 2K pixels wide would be sufficient for most practical purposes, but that precludes any further optical magnification, and may give rise to strong aliasing and moiré effects with some subjects. I think I'd still like to see something in the 5 megapixel region or above personally, but I've used lower-res EVFs in the past without much trouble.</p>

<p>FWIW I find it amazing that we can make anything on the micron scale at all, let alone a miniature TV screen. If we could go back in time along with some modern technology we'd surely be branded as aliens or warlocks.</p>