November 27, 2014, 09:36:45 AM

Author Topic: fast f-numbers  (Read 1028 times)

chromophore

  • PowerShot G1 X II
  • ***
  • Posts: 37
    • View Profile
fast f-numbers
« on: November 19, 2014, 06:39:42 PM »
A recent article from Petapixel about the fastest f-number theoretically possible inspired me to make the following observations about the relationship between f-number and light-gathering ability.

Recall that the f-number is defined as the ratio of the distance between the image plane and the exit pupil, to the diameter of the exit pupil.  For an idealized thin lens, this is equivalent to the focal length divided by the aperture diameter.

Also familiar to most of us is the idea that light-gathering ability doubles for each full stop increase in speed; i.e., f/1.4 gathers twice as much light as f/2, which in turn gathers twice as much light as f/2.8, etc.

When I read the Petapixel article and the commentary therein, it seems that this doubling/halving notion of full stop increments was overlooked and not fully understood.  That is to say, while this relationship between f-number and light-gathering ability is true at relatively slow f-numbers, it is most certainly NOT true at fast f-numbers, because it is an approximation.  f/0.5 is not, strictly speaking, twice as fast as f/0.7, nor is f/0.35 twice as fast as f/0.5, even though the area of the pupil is twice as large.

The true light-gathering ability of a lens is measured not by the f-number but by the square of the angle of incidence of the marginal paraxial rays to the optical axis.  If we think of a light source at infinity, its rays enter the lens (which is also focused at infinity) parallel to the optical axis.  Off-axis rays get refracted to form an image of the light source, and the angle of the cone of light that forms that image point determines the intensity.

In the small-angle case, the tangent of the angle is a good approximation of the angle itself:  theta = tan theta for "sufficiently small" theta.  But if the angle is large--as in the case of very fast lenses--this approximation breaks down, and we can no longer use the f-number as a reliable indicator of how much light is being gathered.  For example, compared to f/1.0, an f-number of f/0.7 is only 1.76 times brighter; f/0.5 is only 1.63 times brighter than f/0.7; and f/0.35 is only 1.48 times brighter than f/0.5.  Of course, it is extremely rare to see even the first case, and we certainly don't see the others, but in the theoretical discussion of the fastest possible lens, it is important to point out that even a theoretical f/0 lens (for which the lens diameter is infinitely large, and the marginal rays somehow manage to make a 90-degree refraction and strike the image plane with no loss), the light-gathering ability is finite.  f/0.35 does not get us 32 times the light-gathering ability of f/2, but only about a 15x increase, even assuming an ideal lens and sensor.  And this is even true at slower f-numbers, though to a much smaller extent:  f/1.0 is really only 13.9x as bright as f/4, not 16x brighter as you would expect  just by counting full stops.

canon rumors FORUM

fast f-numbers
« on: November 19, 2014, 06:39:42 PM »

Mt Spokane Photography

  • EF 50mm F 0.7 IS
  • *********
  • Posts: 9182
    • View Profile
Re: fast f-numbers
« Reply #1 on: November 19, 2014, 07:30:00 PM »
Its even more complex than that.
 
 
You also must take into account light loss in the glass, subject distance, and as far as light reaching the sensor of a digital camera, the micro lenses at the edges of the sensor pickup up less light due to the angle of incidence.
 
http://en.wikipedia.org/wiki/F-number#T-stop
 
 

Cosmicbug

  • Power Shot G7X
  • **
  • Posts: 17
    • View Profile
    • Cosmicbug
Re: fast f-numbers
« Reply #2 on: November 19, 2014, 07:40:51 PM »
Thank god we have TTL metering  :)

ajfotofilmagem

  • 1D X
  • *******
  • Posts: 1071
    • View Profile
Re: fast f-numbers
« Reply #3 on: November 19, 2014, 08:05:21 PM »
Lenses with very bright aperture, F1.2 type provide a small gain in light gathering compared to F1.4. This happens due to the additional light rays reaching the image sensor at a very tilted angle. An F1.0 or more luminous lenses have diminishing returns, and the image quality is very poor.

There is a phenomenon described by a fellow canonrumors that exemplifies these diminishing returns:
He tested a Canon F1.4 lens with the camera set on full manual mode, and then unlocked the lens and turned 2mm for the electrical contacts do not work. So the camera could not identify which lens was mounted, and he repeated the photo as a Canon EF lens would not. At this time the camera prodiziu darker images.

And the explanation was that our friend Neuro Canon compensates for the loss of light rays (that reach the sensor with tilted angle) increasing the ISO in secret. Canon knows that such a model has 1/2 stop loss of light in digital sensors and makes a ISO100 secretly pushed to 150 for example. At the time that the electrical contacts lens were disconnected (by turning the lens a little bit) the body has stopped making this ISO secretly pushed, and the image was darker.

If we look at the transmission of light in F1.2 lens will realize that they are T1.4 and not to frustrate people who paid thousands of dollars for the minimum difference between the núfero "F" and light transmission "T" Canon uses this artifice.

NancyP

  • Canon 7D MK II
  • *****
  • Posts: 475
    • View Profile
Re: fast f-numbers
« Reply #4 on: November 19, 2014, 08:12:54 PM »
T numbers are more accurate, but stills photographers are creatures of habit.

Mt Spokane Photography

  • EF 50mm F 0.7 IS
  • *********
  • Posts: 9182
    • View Profile
Re: fast f-numbers
« Reply #5 on: November 19, 2014, 08:47:34 PM »
T numbers are more accurate, but stills photographers are creatures of habit.

F numbers are accurate for depth of field, T numbers for exposure.
 
Few photographers continue to use manual exposures, the ones that do have learned to adjust exposures to their liking.  I've used manual exposure most of my life, decent auto exposure cameras are relatively new, and there are lots of gotchas that can mess up things. 
 
As we convert to mirrorless, and exposure is taken from the sensor, that should improve things a little.

chromophore

  • PowerShot G1 X II
  • ***
  • Posts: 37
    • View Profile
Re: fast f-numbers
« Reply #6 on: November 19, 2014, 10:28:12 PM »
Its even more complex than that.
 
 
You also must take into account light loss in the glass, subject distance, and as far as light reaching the sensor of a digital camera, the micro lenses at the edges of the sensor pickup up less light due to the angle of incidence.
 
http://en.wikipedia.org/wiki/F-number#T-stop

I am well aware of those considerations.  However, my post was intended to address the geometric optics of fast f-numbers, since real lenses with f-numbers of f/0.35 are not feasible.  My point, as I stated at the beginning, is that the relationship of f-number to light gathering ability is a small-angle approximation, and this phenomenon is completely independent of other issues like transmission and incident light loss due to sensor design.  It is a *geometric* issue.

canon rumors FORUM

Re: fast f-numbers
« Reply #6 on: November 19, 2014, 10:28:12 PM »

Hjalmarg1

  • Canon 70D
  • ****
  • Posts: 305
  • Photo Hobbyist
    • View Profile
Re: fast f-numbers
« Reply #7 on: November 20, 2014, 01:06:07 AM »
Really good information here but seems to be too complex. I am happy cameras have very smart algoritms.
Body: 5DIII. Prime Lenses: 15mm f2.8, 100mm f2.8L IS, 35mm f2 IS, Extender EF 2X III.
Zoom Lenses: 16-35mm f4L IS, 24-70mm f2.8L, 70-200mm f2.8L IS II. Others: Flash 580EX II, 270EX II & MR-14EX II

canon rumors FORUM

Re: fast f-numbers
« Reply #7 on: November 20, 2014, 01:06:07 AM »