Dome Theory 
Dioptre & Focus Distance
Categories: Features, Library, Still Photo [home]Author: Julian Scheunemann (Industry)
dome theory - dioptre & focus distance
A frequently asked question is if a dioptre lens is required with a certain dome/lens combination. The following is a theoretical approach which just could give an idea when choosing a lens/dome combination. This could be important as there are lenses which do not allow mounting a dioptre.
Before determining the minimum required focusing distance some dome design aspects are to be mentioned.
dome design
The radial light rays go thru the dome and meet in a virtual point, called lens entrance pupil or centre of perspective (not one of the nodal points!). Virtual, because the rays are refracted already upon entering. Distance between dome glass and the entrance pupil is equal to the dome radius ( r ) if the dome (and port extension) is correctly designed for a certain lens.
Unfortunately I found only Sigma and Zeiss providing the position of the entrance pupil (Zeiss officially and Sigma Japan on email request.). You also could take a laser pointer to find the position. You can rotate the lens around this point and the red ray would have to go thru the lens (like the pano
shooters do, sometimes it is erroneously called nodal point).
Sigma 12-24mm @12mm, not to scale:
dioptre required?
If a certain lens works without a dioptre it has to be capable of focusing at least to infinity underwater. Therefore it has to be determined how far the virtual image is in front of the dome.
This is influenced by the dome radius. Smaller radius gives a nearer virtual image. Considering the following:
refraction index water = 1.33, refraction index air = 1.0, dome radius = average between outer and inner radius - the simplified formula can be used including these values:
L(inf) = 3.03 * r
L(inf) = distance between dome and virtual image (at underwater infinity).
To be strictly correct the result would have to be a negative value due to the negative refraction index of the dome: L(inf) = -3.03 * r
If the dome thickness (inner and outer radius) would be included into the calculations the distance would even become a little shorter.
Example: dome radius 10cm gives L(inf) = 30.3cm
This is the distance from the dome glass. A lens would have to focus at least to this distance in order to “prevent” a dioptre. The problem is that the lens minimum focusing distance is given from film/sensor plane. You would have to know the distance from the entrance pupil to the film/sensor plane.
A simple and rough way to confirm that the lens should work without a dioptre is to consider the dome radius starts at the middle of the lens (which of course never should be the base for positioning a dome!):
req. min. focusing distance = L(inf) + r (dome radius) + lens length / 2 + flange focal length.
The flange focal length is the distance between the film/sensor plane and the camera bayonet.
For example: Canon = 46.5mm and Nikon = 44mm.
The result is not absolutely correct because the middle of the lens is used instead of the entrance pupil. In general the entrance pupil is more close to the top of the lens
(retrofocus types). So there is still a little headroom with this rough result and the lens should work.
An example if the position of the entrance pupil is known:
Distance film/sensor plane to dome glass, Sigma 12-24mm @12mm, Canon mount:
required min. focusing distance = L(inf) + 4,4cm (flange focal length) + 7,43cm (bayonet to entrance pupil) + r (dome radius)
what dioptre?
Every dome has a certain (negative) focal length. A 'perfect' dioptre would just equalize the dome focal length and restore the lens topside focus capabilities. This is independent from the lens focal length and only predicted by the dome radius:
- 100cm
D = ----------------
- 3.03 * r
Example: Dome radius = 10cm: D = 3.3
This is just theory of course as there are only full or half steps available. So choose the next close value available.
focus distance underwater
Originally my intention was to create some DOF and hyperfocal distance tables for the most common lens/dome setups.
But my effort to get the required values (lens centre of perspective, dome radius, maximum field of view to which the dome radius is constant) was not very successful. It seems to be some kind of company secret.
Just a very small part of the focus range is used on the lens behind a dome port. Therefore it would make no sense to create these tables with some rough values. DOF is very sensitive to little value deviations underwater. In addition DOF is further reduced by the smaller circle of confusion with cropped image sensors ( COC = sensor diagonal / 1500. gives ~ 0,019mm with cropped DSLRs). The dome glass thickness would be necesarry as well.
The following table gives at least an impression how underwater focus distance and lens focus adjustment compare. You can also see the closest possible focusing distance.
Thank you to Sigma Japan and Sea & Sea Japan who are very open minded and have provided some details.
Sea & Sea fisheye dome (the big one) with given radius (105,5mm).
Sigma 15-30mm lens @ 15mm with Canon mount (44mm flange focal length):
Ikelite fisheye dome with radius mentioned in the wetpixel-forum (~ 79mm).Sigma 15-30mm lens @ 15mm with Canon mount (44mm flange focal length):
Julian ("Jolly" on Wetpixel)
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Comment(s):Just a couple of points I’d like to add to this very useful piece. Firstly, the entrance pupil can shift with wide-angle zooms as their focal length changes, so the dome/lens/dioptre set-up may only be optimised for a specific focal length (I’ve found that in practice this is usually the widest setting as this is probably where the lens will be used most!). Secondly, using a dome produces a c’urved image field’ (that is to say that the image on the flat sensor isn’t flat) and roughly speaking, the smaller the dome diameter, the greater the curvature. So corners may simply never be sharp except at extremely small apertures. There is (apparently) empirical evidence which suggests that a simple dioptre lens (curved on the outside surface, flat on the inside or lens side) tends to curve the image field in an opposing direction so can provide better overall correction as well as adjusting for focus. I’ve never looked into the optics of why this is so but must do one day.
In general terms its best to have as big a dome as possible (correctly set up with appropriate extenders) and a lens that has as good close-focus capabilities as possible. For an optical explanation, Sidney Ray has a chapter in his massive volume on photography (which unfortunately costs around £100) which shows the formulae and so on. All that said, it doesn’t take a huge amount of time to check out a lens with various extenders and diopters, and (sadly) there are many, many examples of dome/lens mismatches published which makes one realise that some people never actually seem to notice!Posted by Paul Kay on 10/08 at 04:08 AMPaul,
thank you for the comment.
The issue of focusing on a curved image is seldom taken into consideration. The image centre has the largest focus distance. The corners are always closer in terms of focus distance.
Huge radius is the best way to minimize this problem and finally of course resulting in diameter increase depending on the Dome’s max. field of view (curvature angle) – controversial to some available dome designs in the industry.As I understand this does not apply to fisheye lenses as they focus in a manner the virtual image is shaped. Another reason to enjoy them.
Sigma 15-30’s entrance pupil shift is a bit more than 2cm when zooming from 15 to 30.
Agree, match should go with the wide position. Zooming towards 30mm reduces the corner issue as the field of view becomes smaller. 30mm itself is non critical as many would house it behind flat glass. So 2cm in this lens example should be fine when still behind a dome glass. On a cropped camera even more.Julian
Posted by Julian on 10/16 at 07:33 AM-
Posted by Paul Kay on 10/28 at 05:35 AM
You might be interested to take a look at http://www.canon.com/camera-museum/ where some Canon lenses are shown in diagramatic form. Assuming that they are dimensionally correct (ie to scale) then it should be possible to get some idea of the position of the entrance pupil. Unfortunately the zooms are only shown at one setting and its focal length is not stated, but it is not too much of a problem to figure out with the lens in front of you. I started to sort out similar data to that you produced above for Canon’s 17~40mm lens and will post it when I’ve got sufficient details calculated. There is undoubtedly a similar shift to that of the Sigma and the lens tends to exhibit poor corners behind a small dome.
Posted by Paul Kay on 10/28 at 05:41 AMThere is a nice procedure to obtain those data (without lens manufactures providing them). According to your equipment signature you might already enjoy the results :-) I’ll send you an email.
Posted by Julian on 11/02 at 09:00 AMJoe Wisniewski gives a nice table, including entrance pupil data at:
http://www.swissarmyfork.com/lens_table_1.htm
Interestingly, about 4mm's of change over the focal range of the Nikon 12-24 (avg about 110 mm)—all relative to lens flange.Also, “plattro” at http://www.kekus.com/forum/showthread.php?t=329&goto=nextoldest says
the Nikon 10.5 has En of 87mm and the 14/2.8 is 97 mm (both +/- 5mm).I'm still shopping for WA DSLR stuff, but it'd be interesting to know if the ports we see make sense with respect to these measurements.
Posted by Chris White on 01/31 at 10:27 AMOf course you can “see” the entrance pupil when you look at a lens. If you shine a light through the viewfinder, hence running the optical path in reverse, you can see it emerge from the entrance pupil, looking at the front of the lens. If you then hold up an empty toilet paper/smarties tube to the surface of the port (round near the edge of the glass), you can evaluate how close the pupil is to the centre of curvature. Most Ports don’t let you get a fisheye in the right place due to the port flange placement.
That’s what my O-level Physics is telling me, so if an optics guru can show me what I’ve got wrong I’d love to know :)
Posted by Rattus on 09/29 at 06:26 AM
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