f-values in camera is calculated using formula:

  f = focal_length / lens_diameter

We know that focal blur on Pov-Ray is maded shooting rays from cube and cube
side width is aperture value. We have to calculate some area where to shoot
rays. If we draw light rays in camera (real world camera) and straight line
from center of lens to focal point we can see angle between line and focal
point. The angle can be solved using atan:

  tan(angle) = (lens_diameter / 2) / focal_length

  tan(angle) = 1 / (f * 2)

  angle = atan(1 / (f * 2))

Using this angle we can draw a lens as circle if we know focal_length. If we
use this angle in focal point outside the camera, we can draw area as
sphere where to shot rays to get focal blur.

  r = distance_to_focal_point * tan(angle)

  r = distance_to_focal_point * tan(atan(1 / (2 * f))

  r = distance_to_focal_point / (f * 2)

Aperture area in Pov-Ray is cube. We have to solve equation to get cube side
width from sphere volume.

  x ^ 3 = pi * r ^ 3 * 4 / 3

  x = r * (pi * 36) ^ (1/3) / 3


Final equation when we put distance_to_focal_point / (f * 2) to r is:

  aperture = distance_to_focal_point / (f * 2) * (pi * 36) ^ (1/3) / 3

After simplify:

  aperture = distance_to_focal_point * (pi * 36) ^ (1/3) / (f * 6)


Comments and corrections please.

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Matti Karnaattu wrote:
>f-values in camera is calculated using formula:
>
>  f = focal_length / lens_diameter
>
>We know that focal blur on Pov-Ray is maded shooting rays from cube and cube
>side width is aperture value.

>Aperture area in Pov-Ray is cube. We have to solve equation to get cube side
>width from sphere volume.
>
>  x ^ 3 = pi * r ^ 3 * 4 / 3
>
>  x = r * (pi * 36) ^ (1/3) / 3
>

The "aperture" in PovRay is a square, not a cube.  And the area used by a
camera lens is a circle, not a sphere.

And if you use 37 or fewer blur samples, the "aperture" in PovRay is
actually a hexagon, which is even closer to being a circle than a square
is.

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>The "aperture" in PovRay is a square, not a cube.  And the area used by a
>camera lens is a circle, not a sphere.

I know that area used by in camera lens is circle but I dont know that
Pov-Ray uses square. That's why I use circle in my calculations because I
tried to fit area to cube :)

Thanks for correction. Here is new formula:

  aperture = distance_to_focal_point * pi ^ (1/2) / (f * 2)

Matti

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"Matti Karnaattu" <nomail@nomail> wrote:
> >The "aperture" in PovRay is a square, not a cube.  And the area used by a
> >camera lens is a circle, not a sphere.
>
> I know that area used by in camera lens is circle but I dont know that
> Pov-Ray uses square. That's why I use circle in my calculations because I
> tried to fit area to cube :)
>
> Thanks for correction. Here is new formula:
>
>   aperture = distance_to_focal_point * pi ^ (1/2) / (f * 2)
>
> Matti

Just found this website while searching on Google...thought you guys might
be able to answer a question I have regarding aperture values on cameras.
I am aware that the f-stop refers to the number of times the apertures
diameter fits into the focal length of the lens, but what I don't
understand is the change in f-stops with a zoom lens with a floating
aperture.
ie a 28 - 80 mm lens with a max aperture of f3.5, max aperture at 28mm =
28mm/3.5 = 8mm diameter.  This seems way too small.  Also, if the max
aperture on this same lens changes to say f5.6 at 80 mm then the max
aperture's diameter at this focal length = 80mm/5.6 = 14.3 mm...
I'm confused - can anyone out there explain this for me?
(I will be eternally in your debt...oh, and what the hell is a POVray?)

Fenris

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