# Shape of largest die that fits on reticle

By: Adrian (a.delete@this.acm.org), July 8, 2022 10:18 pm
anonymou5 (no.delete@this.spam.com) on July 8, 2022 10:29 am wrote:
> Math Nerd (math.nerd.delete@this.nerds.com) on July 8, 2022 4:57 am wrote:
> > Why is the largest die that fits on a reticle a rectangle
> > (26mm x 33mm)? I expected it to be a square because
> > I thought the optics would be circularly symmetrical and a square is closer to a circle than a rectangle.
>
> https://en.wikipedia.org/wiki/Digital_camera
> https://en.wikipedia.org/wiki/Image_sensor_format
> https://en.wikipedia.org/wiki/Full-frame_DSLR
>
> Don't look at it through a binary cause-vs-effect lense though.
>
> Maybe more along the lines of "this is what things have gravitated towards over time".

For images intended to be viewed by humans, the reasons for choosing an aspect ratio have been very different and completely unrelated to any reason for choosing an aspect ratio in photolithography.

The aspect ratio of 4:3, which was used in the older television, monitors and for many formats of still photography and cinematography, had its origins in some old research results.

There have been some experiments to determine the largest solid angle in which an image can be seen as a whole by humans, while perceiving accurately the perspective relationships between the objects seen in the image.

The results have been that this solid angle is approximately that of the vertex of a pyramid having as base a rectangle with the aspect ratio 4:3 and with the height being the double of the smaller side of the rectangle (e.g. a pyramid having the lengths of the base sides as 6 and 8, and the length of the other 4 edges 13, and the pyramid height 12).

These results have provided justification for both the 4:3 aspect ratio and for the focal length of a "normal lens".

A "normal lens" is now usually described as having a focal length approximately equal to the image diagonal. This definition is used because using the diagonal makes it independent of the aspect ratio chosen for the image, which might be, e.g., 3:2 or 5:4 instead of 4:3. Nevertheless, the normal focal length determined in the original research was 20% greater than the diagonal, not equal to the diagonal.

The actual focal length of "normal" lenses has always been closer to the original research results and not to the definition simplified to be easily remembered by the masses. For example, an image of 24 mm x 36 mm, on 35 mm film, has a diagonal of 43 mm, but the focal length of a "normal lens" is usually between 50 and 58 mm, i.e. corresponding to the 52 mm given by the original research results.

The other most popular aspect ratio used in photography, 3:2, has already been used in various photographic films or photographic glass plates during the 19th century, but at that time many other aspect ratios between 1 and 2 were also in use. I have no idea how the choices for aspect ratios were made during that time.

I suppose that the later preponderance of the 3:2 and 4:3 aspect ratios has been due to the fact that using these 2 aspect ratios, it is possible to divide as much as desired a larger image format, alternating between these 2 ratios, e.g. an 18 x 24 photographic paper can be divided into two 12 x 18, then into four 9 x 12, then into eight 6 x 9, and so on, similarly to the ISO paper formats that use the sqrt(2) aspect ratio.

TopicPosted ByDate
Shape of largest die that fits on reticleMath Nerd2022/07/08 04:57 AM
Shape of largest die that fits on reticleDoug S2022/07/08 06:39 AM
Shape of largest die that fits on reticleMark Roulo2022/07/08 09:09 AM
Shape of largest die that fits on reticleanonymou52022/07/08 10:29 AM
Shape of largest die that fits on reticleAdrian2022/07/08 10:18 PM
Shape of largest die that fits on reticleDavid Hess2022/07/14 04:28 PM