Teleconverters and Aperture

 

Effective Aperture with Teleconverters:  Optical Analysis


There has been discussion on the DPR Panasonic Forum regarding the effect on aperture when a teleconverter (TC) is mounted on the front of a digicam such as the FZ35/38.  Some people have suggested that there is a loss of light of 1-2 stops while it has also been claimed that there can be a gain in f stops.


While Shene has described the optics of the "Galilean telescope" type front-mounted TC on his webpage (http://www.cs.mtu.edu/~shene/DigiCam/index.html), he has not explicitly examined the effect on aperture there, although this is likely to be simply because in fact such a TC has no effect on aperture.


I am indebted to Dr J. C. Brown for providing the following optical analysis, which he also posted on the DPR Panasonic Forum at:  http://forums.dpreview.com/forums/read.asp?forum=1033&message=37230951

He also added some further comments in that thread in response to replies.  As Jimmy explains below, the use of an afocal TC will not result in either an increase or a decrease in the effective aperture of the camera lens.



Effect on aperture of adding a front mounted TC 

By Dr J. C. Brown


Here it is assumed that the light received by the camera and TC is radiated uniformly from a sufficiently large circular area at a long distance from the camera. A circular area of uniformly bright sky would be a reasonable approximation.


The ray diagram below is for a 1.5X afocal TC, a "Galilean telescope" consisting of convex and a concave lenses with their focal points coincident and their focal lengths in the ratio of 1.5 to 1. The traditional analysis assumes that the light rays entering the front lens are parallel as they come from infinity and those leaving the rear lens are parallel because of the optical arrangement of the lenses. Consequently the intensity of the beam leaving the rear element of the TC is greater than that of the beam entering the front element by a factor of 2.25, 1.5 squared.


1.5x Afocal Teleconverter


In the diagram you will see that the black lines which show the traditional light path used in the analysis do not enter the front element of the camera lens, indicating some loss of light. You will also see that for the black, green and red lines the ratio of the diameter of the beam entering the TC to that of the corresponding beam leaving the TC is 1.5. It should be noted here that these green and red lines correspond to cylinders of parallel light which come to a focus at a single point at the centre of the sensor.


The most important point to note about the behaviour of the TC is that, as illustrated in the ray diagram, in addition to reducing the diameter of the cylinder of light passing through it by a factor of 1.5, the TC also reduces the field of view of the camera by the same factor. These fields of view are of course cones with their apex at the focal point of the camera lens. This is shown schematically in the diagram as a FOV of 7.76 degrees for the camera on its own and a FOV of 5.18 degrees for the camera with the TC attached.


Consequently at a suitably long distance from camera, the diameter of the circle which corresponds to the field of view of the TC is 1.5 times smaller than the diameter of the circle which corresponds to the field of view of the camera on its own. Due to the difference in the circular areas enclosed by their respective fields of view the total amount of light entering the camera without the TC will be greater than the total amount of light entering the TC by a factor of 2.25, 1.5 squared.


Thus the increase in intensity due to the reduction in diameter of the light passing through the TC cancels exactly the loss of intensity due to the reduced field of view, with the result that the total amount of light passing through the camera lens to the sensor is exactly the same with the TC as it is without the TC. There is therefore neither an increase nor a decrease in the effective aperture due to the addition of an afocal TC.




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