Why has the 500mm f8 mirror reflex lens such shallow DoF?

[Chris Malcolm]

I have other lenses which operate at 250mm and 400mm, and often use them at f8. Extrapolating from those other lenses I get the distinct impression that Sony's 500mm catadioptric reflex lens has a sharper shallower DoF than I'd expect from an f8 lens of that focal length.

It occurs to me that since the doughnut bokeh is visually fiercer and more visually obtrusive than a smooth even bokeh, that it will make this lens more aesthetically unforgiving of the slight blurring of being slightly off focus, which will also reduce the effective DoF.

It also occurs to me that while the 500mm is f8 in terms of light gathering ability, it's wider optically than an f8 would be if it didn't have that hole in the middle. It looks to me as though the "lens" diameter is 80mm, and the hole in the middle is 32mm diameter. If we assume that apparent diameter to be the same as the effective diameter then that hole reduces the light gathering power to that which would be produced by a lens of sqrt(80^2-32^2) = 73.3mm. That suggests that because of the hole in the middle for purposes of depth of field the lens has an effective aperture of f7.3.

But I'm confused here because a 500mm f8 lens would have an effective diameter of 62.5mm. So there's something wrong with the assumptions behind my arithmetic, and I'm left simply with the unquantifiable idea that this lens with its hole in the middle will be optically of effectively wider aperture than
its effective light gathering aperture.

Can anyone correct my arithmetic or reasoning here?

[harvey]

I have other lenses which operate at 250mm and 400mm, and often use them at f8. Extrapolating from those other lenses I get the distinct impression that Sony's 500mm catadioptric reflex lens has a sharper shallower DoF than I'd expect from an f8 lens of that focal length.

Is your extrapolation out of line with what one of the online DOF calculators would give? For example I just tried the one at this site.

Code: Select all

  lens (mm)      250      400      500  
  DOF (5m)        18        7        4
  DOF (10m)       75       29       18  
  DOF (20m)      305      118       75

where DOF is in cm for f/8 and a 35mm-sized format. I have no idea how accurate their formulas are but it seems you only have two data points to go on.

Harvey

[David Kilpatrick]

Sure, the depth of field is determined by the largest diameter (outer) of the mirror lens system. You could make an f/8 mirror lens 100mm in diameter with an even bigger central mirror and more of an annular effect, it would still be f/8 but but have the same depth of field as a conventional 500mm f/5.6.

The Sony cat has an effective aperture approx f/6.3 for depth of field purposes - which is how it is able to work with AF. And yes, it has shallower depth of field than a 500mm f/8 dioptric lens.

David

[01af]

Can anyone correct my arithmetic or reasoning here?

Nobody can. Because both your arithmetic and your reasoning are perfectly correct.

It's your metering that's off. According to my measurements, the outer diameter of the AF Reflex's entry pupil is 71 mm; the diameter of the secondary mirror is 32.5 mm. So the area of the donut-shaped entry pupil is the same as a regular 63.1 mm circle which translates to a geometric aperture of 1:7.92 (provided the nominal value of 500 mm for the focal length is accurate).

For exposure, the entry pupil's area is definitive. For depth-of-field (and focusing, too), it's the entry pupil's outer diameter which matters---it resembles that of a 1:7.0 lens.

By the way, now after having measured the diameters fairly accurately, I am surprised that the obstruction caused by the secondary mirror is decreasing the effective aperture by such a small amount. I always thought it was somewhere between 1/2 and one f-stop but in fact, 1:7.9 versus 1:7 means a difference of merely 1/3 of an f-stop. In terms of depth-of-field, this should be hardly noticable in photographs. I guess the reason why the DOF appears narrower is because with the harsh bokeh, the borderline between in-focus and out-of-focus is more obvious to the eye of the beholder.

-- Olaf

[Chris Malcolm]

Can anyone correct my arithmetic or reasoning here?

Nobody can. Because both your arithmetic and your reasoning are perfectly correct.

It's your metering that's off. According to my measurements, the outer diameter of the AF Reflex's entry pupil is 71 mm; the diameter of the secondary mirror is 32.5 mm. So the area of the donut-shaped entry pupil is the same as a regular 63.1 mm circle which translates to a geometric aperture of 1:7.92 (provided the nominal value of 500 mm for the focal length is accurate).

Thanks! But how did you measure the entry pupil? I just guessed it would be close to the physical diameter of the glass because I didn't know how to measure the pupil.

For exposure, the entry pupil's area is definitive. For depth-of-field (and focusing, too), it's the entry pupil's outer diameter which matters---it resembles that of a 1:7.0 lens.

By the way, now after having measured the diameters fairly accurately, I am surprised that the obstruction caused by the secondary mirror is decreasing the effective aperture by such a small amount. I always thought it was somewhere between 1/2 and one f-stop but in fact, 1:7.9 versus 1:7 means a difference of merely 1/3 of an f-stop. In terms of depth-of-field, this should be hardly noticable in photographs. I guess the reason why the DOF appears narrower is because with the harsh bokeh, the borderline between in-focus and out-of-focus is more obvious to the eye of the beholder.

So my figures weren't quite right, but my general puzzlement was: the amount lost by the central mirror hole isn't nearly enough to explain the apparent shallowness of the DoF compared to normal refractive lenses of similar length. Maybe the central mirror hole isn't the size of the real loss, but something which fits inside it?

I don't know if the shape of the bokeh doughnuts gives us a suggestion of a clue. I thought they were simply supposed to mirror the shape of the lens aperture, but the doughnuts seem to have holes which are bigger than the appearance of the lens head on or your measurements suggest.

--
Chris

[01af]

... how did you measure the entry pupil?

I removed the lens caps and placed the AF Reflex lens on the window sill, along with a ruler right next to it. Then I took a photograph of the AF Reflex lens from a distance of approx. 7 m/20 ft, with the camera's optical axis aligned with the AF Reflex lens'. Then the entry pupil simply is the bright area visible inside the lens. In Photoshop, I used the Ruler tool to measure the diameters and compared their dimensions in pixels to the image of the ruler. This way you'll get the entry pupil's diameters with an accuracy down to a few tenths of a millimeter.

... the amount lost by the central mirror hole isn't nearly enough to explain the apparent shallowness of the DoF [...] I don't know if the shape of the bokeh doughnuts gives us a suggestion of a clue.

Neither know I. In my previous post, I was only speculating about this point.

I thought they were simply supposed to mirror the shape of the lens aperture ...

Yes, exactly.

... but the doughnuts seem to have holes which are bigger than the appearance of the lens head on or your measurements suggest.

Ummm ... maybe (just speculating again) this has to do with the difference of the distances of the focus plane and the out-of-focus highlights. At different distances, the shape of the entry pupil (the ratio of inner to outer diameters in particular) might differ. So when the lens is focused at, say, 5 m then the remote background at 100 m may 'see' a different entry pupil ...

I'll check that hypothesis as soon as I have some time to spare. I'll meter the entry pupil by the method outlined above twice; once with the lens focused at me (i. e. at 7 m or so) and once with the lens focused at infinity. If it makes a difference then possibly that'll be the explanation to your issue (or part thereof).

However---when thinking about it---an increased inner diameter, i. e. a bigger hole in the donuts, would not reduce depth-of-field; it would just reduce brightness. For the DOF to become shallower, it would take the outer diameter to increase.

-- Olaf

[Javelin]

wouldn't the void in the center of the rings be caused by the mirror? I mean before the light goes through the aperture it is reflected off a mirror with a hole in the middle and the objective end has a void in the middle too for the other mirror since the bokeh shapes are all the same as the internal parts of the lens doesn't it stand to reason these reflex lenses will have the same reflections only with voids in the middle? if the holds in the mirror and the reflex mirror were rectangular would the bokeh be 4 cornered donuts?

[jcoffin]

However---when thinking about it---an increased inner diameter, i. e. a bigger hole in the donuts, would not reduce depth-of-field; it would just reduce brightness. For the DOF to become shallower, it would take the outer diameter to increase.

-- Olaf

Actually, that's not true. With a normal lens, the image is formed from light that's following the paths through the lens UP TO the aperture you've set. For example, if you set the aperture to f/2, you're getting some light that follows the same path through the lens that it would if the aperture was set to f/16 -- and that light following that f/16 path through the lens has exactly the same characteristics as it would if the aperture was set of f/16. All that's happening when you adjust the aperture is that you're removing the light that would follow the other paths through the lens that result in less depth of field. In the case of f/16 vs. f/2 (for example) the center portion makes essentially no visible contribution to the picture -- so little light is going through that central portion that it's underexposed too much to make any difference to the picture.

In the case of the 500 f/8 reflex, however, the center obstruction is fairly large -- assuming your 32.5 mm number is correct (I haven't checked) that portion of the light path would be approximately f/15. Since it's an f/8 lens, that means the center portion that would contribute about 1/4th of the exposure if it wasn't blocked. Looking at it from the other direction, the light following that path would be underexposed by 2 stops -- in other words, it would still be making a visible contribution to the picture.

[zomerzetjlam]

I have a Samyang 800mm mirror lens which obviously has a very short dof but what makes it most frustrating is that after setting up a shot the screen on my Alpha 100 keeps saying no lens attached!! any suggestions?

[David Kilpatrick]

Go into the menus and set the camera to allow shutter release with no lens attached...

That will remove the message!

David

[Chris Malcolm]

However---when thinking about it---an increased inner diameter, i. e. a bigger hole in the donuts, would not reduce depth-of-field; it would just reduce brightness. For the DOF to become shallower, it would take the outer diameter to increase.

-- Olaf

Actually, that's not true. With a normal lens, the image is formed from light that's following the paths through the lens UP TO the aperture you've set. For example, if you set the aperture to f/2, you're getting some light that follows the same path through the lens that it would if the aperture was set to f/16 -- and that light following that f/16 path through the lens has exactly the same characteristics as it would if the aperture was set of f/16. All that's happening when you adjust the aperture is that you're removing the light that would follow the other paths through the lens that result in less depth of field. In the case of f/16 vs. f/2 (for example) the center portion makes essentially no visible contribution to the picture -- so little light is going through that central portion that it's underexposed too much to make any difference to the picture.

In the case of the 500 f/8 reflex, however, the center obstruction is fairly large -- assuming your 32.5 mm number is correct (I haven't checked) that portion of the light path would be approximately f/15. Since it's an f/8 lens, that means the center portion that would contribute about 1/4th of the exposure if it wasn't blocked. Looking at it from the other direction, the light following that path would be underexposed by 2 stops -- in other words, it would still be making a visible contribution to the picture.

So the central obstruction removes the central portion which would have greatest depth of field, and in compensation adds some extra at the edge with less depth of field. So as well as having the shallow depth of field due to the width of the lens being around f7, it has also lost the longer depth of field contribution of the centre of the lens, thus sharpening the transition at the boundary of the depth of field.

That's an idea I hadn't thought of, or seen mentioned elsewhere. Thanks!