Warning : picture spam bellow
rjlittlefield wrote:I think that the circles are sized to exactly contain the aperture (on the left), to just touch the sensor (on the right), and to scale linearly at the intermediate points.
It's that but I didn't sized them, they are the section of the aperture cone at 3 positions on the lens-sensor axis (1/4, 1/2 and 3/4). The section plane is perpendicular to the lens-sensor axis.
rjlittlefield wrote:Similarly, the rectangles are sized to exactly contain the sensor (on the right), to scale linearly at the intermediate points, and to just touch the aperture (on the left). The rectangle touching the aperture is not drawn.
In fact the only rectangle of the left drawing is the sensor. What you see here are rectangles with rounded corners.
This time, what you are seeing is the section of the volume containing all the direct rays between the lens and the sensor. These pseudo rectangles are, too, the result of the intersection with the 3 section planes (at 1/4, 1/2, 3/4). There is no rectangle at the lens level because, at this position, the section of this volume is a circle.
I think that you thought that these rectangles was the representation of an eventual rectangular baffle. This is not the case (for clarity, i didn't drawed this volume).
I realize that the volume of good rays (purple/magenta volume of direct rays between the lens aperture and the sensor - I will say good rays now
), may be hard to apprehend so I will detail it's construction.
First I put the lens aperture, the sensor and the circumsribing circle to the sensor :
The green circle is just a construction object to create the following cone :
This cone is the envelope of 'good rays' hitting the sensor and lost rays which are focused outside the sensor. This cone, too, describes the minimal diameter of an iris inserted on the lens-sensor axis. If the diameter of the iris is smaller than the diameter of the cone we will have vignetting.
Now with this cone I can create the volume of 'good rays'. I just need to take my better sharpened razor blade and cut the parts focusing outside of the sensor
. For that, for each of the 4 sides of the sensor rectangle, i create a plane which is tangent to the lens aperture circle :
And I cut the external part. The result (after the 4 cut) is the volume that we needed :
Here are other views with sections added to help the visualisation of this volume :
(lens is near us, sensor further)
(sensor is near us, lens is further)
As you can see, as we walk away from the lens, the section is quickly like a rectangle (with rounded corners). It only become a real rectangle when we arrive at the sensor. Beware that, on the drawing, the corners may look like straight oblique lines, but it's not the case. They really are arcs.
This new volume allows us to know the perfect shape of a baffle so that :
- it let pass all 'good rays' to avoid vignetting
- it fits perfectly the volume of 'good rays' to avoid unnecessary opening for stray rays.
The projection of this volume on the section plans is what I've called in my previous post 'perfect' (surface).
rjlittlefield wrote: The exact shape (I think!) would be the boundary of the convolution of two shapes. One shape would be the aperture, scaled from full size on the left to a single point on the right. The other shape would be the sensor, scaled from full size on the right to a single point on the left. When the aperture is a circle, the boundary of the convolution will not have any sharp corners at the intermediate distances. This contrasts with the simple intersection of a circle and a rectangle, which has 8 sharp corners.
You could closely approximate the perfect shape for any shape aperture by counting rays in a discrete simulation:
for each point Pa in the aperture
for each point Ps in the sensor
compute point Pb in the plane of the baffle, on the ray from Pa to Ps
The perfect shape is then all those points in the plane of the baffle where no rays pass.
You're right!! But I Think the result of your computation will gives you the same volume
In fact my volume is the union of all your small cones.
I Think I'm right because :
- for each point in my volume I can find a straight line between the lens aperture and the sensor
- I can't find any straight line between the lens aperture and the sensor outside of my volume.
Now the analysing : the right part of my previous post drawing.
In this part I copied the 3 sections that I got at 1/4, 1/2 and 3/4.
For section 3/4 I had this shape :
In Green/Black we find the perfect surface containing all the good rays that hit the sensor.
I want to compare circle baffle and rectangular baffle.
With a circle baffle :
The circle is the shape of a best fitting circle baffle (explained above), it contains 'good rays' (green/dark) and lost rays (in yellow).
For a rectangle baffle, we need to extend the border of the rounded corner perfect surface and we'll get our best fitting rectangle.
Here is the result :
Now we have all what we need to compare the efficience of circle with rectangle.
I just had to measure the surface of each colors.
For example at 3/4 :
- the surface of the perfect surface (green/black) is 212.7mm².
- the surface of lost rays with a circle baffle is the sum of the 4 yellow surfaces (78.4mm²). It's 37% more than the perfect surface.
- the surface of lost rays with a rectangular baffle is the sum of the 4 magenta/purple corners (10.8mm²). It's 5% more than the perfect surface.
The conclusion of these measures is that : between the sensor and 3/4 of the distance to the lens, the rectangle baffle is with no doubt better than the circle one (as there is far less lost rays surface).
What is really instersting is that, by determinig the volume of 'good rays' we are now able to describe the best fit for a circle baffle and a rectangular baffle. I did it experimentaly (with drawings) but now I can see that all that is simple geometry mathematics. And it's possible to calculate easily the following things :
- diameter of the best fit circle baffle in fonction of it's position on the axis
- width and height of best fit rectangular baffle in function of it's position on the axis
- and, really interesting, the position from which it's better to have a circle baffle or a rectangular baffle (comparison of surface).
So far, I have not considered the positionning to avoid stray rays. I just compare circle and rectangle.