# Depth of field in projection

1. Jan 5, 2012

### tobistobi

Dear all,

I have a question concerning Depth of Field –*I'm trying to find a depth of field calculation method that applies for video projection. Background info is that I often have projection on non-planar surfaces and like to find a method that allows to calculate (without trying out) if with a given video projector (and lens) and a projection distance and a minimum audience distance a projection is still perceived as being in acceptable focus.

I tried to use calculations from photography optics but the results do not match my mock up tests –*I know that focus is something very subjective –*but the results shouldn't differ by factor up to 20.

I started out using the calculation method by Mike Powell http://www.mycockpit.org/forums/content.php/269-Depth-of-Field
but the result I calculated (for a 30mm LCD chip, 49mm lens @fstop 1.7 and a projection distance of 2.4m) was much too small compared what I perceived in a try out with the projector.

Other calculation methods using photography calculations also yielded no better (and not the same!) results.

Is there any method to calculate this? And why does it not correspond with photography calculations?

tobistobi

2. Jan 5, 2012

### schip666!

Depth of Field is a subjective measurement. The photographic calculations I've seen (but don't remember ever actually working out) are based on a "circle-of-confusion" whose diameter is the minimum the "normal" eye can resolve at whatever distance is being discussed... If your image size or viewing distance changes, the circle diameter changes too... The circle size is usually derived with an angle of view from the retina through the eye's lens -- basically the reverse of the light cone in the images on your ref'd page, where the "unfocused" segment would be that minimum circle-of-confusion.

The page picks a '8 * 0.01” = 0.08”' size out of a hat for the circle, which may be correct for the viewing distance he's dealing with. Unfortunately I don't remember where or what the original eye angle is anymore, but you should be able to find it and reverse engineer his calculations appropriately.

You should also consider the resolution of your projection, and maybe the overall sharpness of the lens you are using, as both will probably be in the neighborhood of the DOF resolving value.

3. Jan 5, 2012

### tobistobi

Dear Schipp666,

CoC is pretty clear in literature as the value that at average an eye can distinguish different horizontal lines (line resolution) which is about .2 mm at a viewing distance of 25 cm (considering a high res print). It's linear with distance, so at one meter it's about .8mm. That corresponds –*luckily –*with the rule of thumb that the pixel resolution of a screen [in mm] should be less than the viewers distance [in m].

Yes it's subjective, but it works pretty well in photography.

When going closer than that I can see still details in the pixel dots, so the lens resolution is actually better (or from my perspective even much better) than the projector resolution and enough to be better than the resolution needed to stay under the CoC size.

The resolution of the projector is another –*and in my eyes perhaps the important –*question. Basically Pixel size is often very close to CoC value which could be a reason for perceiving a much larger DOF than calculated. But I found no literature on that effect –*so if any hint I would be more than happy.

thanks, tobistobi

4. Jan 5, 2012

### Andy Resnick

I'm having a little trouble following your post, but it seems that all you need to do is reverse directions.

That is, if you consider your object plane to be the image plane, then your depth of field calculation will make sense- but remember to use the correct focal length and aperture, which will not be the numbers printed on the projection lens, IIRC. You should set the CoC based on your object size as well.

Interesting application!

5. Jan 6, 2012

### tobistobi

Dear Andy Resnick,

thanks for your reply. Yes, reversing is what I thought too, but it does just not fit with what I perceive in the test build up.

Is there a simple and quick way to assess if the f-stop number and focal length of a projection lens of a digital video projector varies from what's stated and if yes, if it's a significant difference?

thanks & best,
tobistobi

6. Jan 6, 2012

### Andy Resnick

I keep getting turned around backwards when I try to think about this because front and rear are reversed... conceptually, I am going to treat the projected image as the 'object', and the LCD as the image plane. The lens information printed on the lens (e.g. 100mm f/2.8) may be the correct information to use, but it may also be for the 'wrong' side since this is a projector lens rather than a camera lens.

If you can't take the lens out and measure it, then you can make some estimates. First, focus the projector to infinity- put the image as far away as you can. Then the distance from the LCD to the aperture stop (about the middle of the lens if there's no stop) is the focal length. The f-number is then given by the focal length divided by the diameter of the exit pupil (the diameter of the front piece of glass- the last glass element before you are outside of the projector).

You also need to know the size of the LCD, because that is used to calculate the size of the CoC. If you want to simply use the printed information on the lens, you may need to also scale the focal length by the size of the LCD relative to a 35mm image size- some online calculators will do this, but some don't.

Can you provide some specifics- projector model, lens information, etc?