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I know that a larger aperture corresponds to a brighter exposure and shallower depth of field for a given focal length.

Is it optically possible for a custom-built camera to form an image with both a reasonably deep depth of field and a very bright image (lots of light gathering)? Is it simply a matter of lens shape and size and camera body dimensions?

Assume that I don't care about the practicality of the resulting camera or the size of the resulting image (e.g, if the camera needs to be the size of a car and the image is 35mm, I'm still interested).

The reason I'm asking is because I've been working on perfecting the anthotype printing process using ordinary plant chlorophyll and common household materials, and I've got it to the point where beautiful prints can occur in about 15-20 minutes of direct sunlight. I would love to build a camera that can take photographs using my "homemade film" (extremely low ISO), even if it takes ~12 hour exposures of still life on a bright day. But I know that I will need the camera to form a much brighter image on the film than most cameras do, since I will need to get within a couple of orders of magnitude of the brightness of direct sunlight.

Edit: to clarify, I am asking about optical physics and geometry, nothing to do with image sensors or exposure time. When I say I want a bright image, I'm talking about the light that falls ON the image sensor. I know that increasing exposure time and sensor sensitivity will help, but that's not what I'm asking about.

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TL;DR: You can't make a large lens to increase the brightness, but you can increase your depth of field by focusing at or beyond the hyperfocal distance.


You didn't say what you were photographing, but with anthotype, cyanotype, etc., I imagine you're probably just trying to get basic photos of mostly static things. Landscapes/cityscapes, pictures of buildings, etc., because of the very low ISO and hence long exposure time requirements. Most likely not macro subjects.

Intended subject, or more specifically, subject distance from the camera, is important if depth of field is a concern. If your subjects are what I've assumed they are, make yourself familiar with the concept of hyerpfocal distance, the camera-to-subject distance where depth of field is mathematically infinite. When your subject is at the hyperfocal distance, everything between half the hyperfocal distance to "infinity" is within your depth of field. The hyperfocal distance H is given by,

H = ƒ2 / Nc

where ƒ is the lens's focal length; N is the ƒ-number (relative aperture) of the lens; and c is the circle of confusion diameter, sort of a quantifier of desired resolution or acuity. For 35mm film cameras, c = 0.03 mm is a good estimate. For higher megapixel crop- and smaller sensor digital cameras, values as low as c = 0.005 mm are stated.

See also:

Aside: Just because hyperfocal distance is a thing, doesn't mean that you should always shoot for it (at least, given a regular camera with ISO options). Personally, shooting with a DSLR or mirrorless camera, I consider hyperfocal distance as a mathematical option, but nothing that I aim for. I focus on my subject, and tradeoff shutter speed and aperture as needed to achieve the look that I'm seeking. But if your goal is to maximize depth of field, hyperfocal distance focusing is a starting point.


As far as image brightness is concerned, understand that photometric exposure, sort of the amount of photons available to capture on your film or image sensor (given constant illumination from the scene), is determined by only two factors: relative aperture N (ƒ number), and exposure time t (shutter speed). Specifically, exposure value, EV, is defined by:

EV = log2(N2 / t)

See EV at Wikipedia

This means that for a given combination of t and N, if you change, say, t by a factor of 2 (i.e., halving exposure time from 60 seconds to 30 seconds), to have the same exposure on your film, you need to compensate by decreasing N by a factor of 1.414... (i.e., square root of 2). This is the fundamental tradeoff between relative aperture and exposure time.

See also:


Regarding your question,

Is it optically possible for a custom-built camera to form an image with both a reasonably deep depth of field and a very bright image (lots of light gathering)? Is it simply a matter of lens shape and size and camera body dimensions?

The fastest lens that is mathematically (but probably not physically) possible is ƒ/0.5.Note. This is due to the conservation of étendue. It's a difficult concept to understand, but see the following questions and links:

See also étendue at Wikipedia. Also, the XKCD What If? explainer, Fire From Moonlight: Can you use a magnifying glass and moonlight to light a fire? is very salient to your question. When you said,


Thus, no matter what sort of lens you construct, you will never be able to have a relative aperture faster than ƒ/0.5. The fastest production lens was the Carl Zeiss ƒ/0.7. Only 10 were ever made – six were sold to NASA, Zeiss kept one for himself, and three were bought by Stanley Kubrick for use in filming Barry Lyndon (see: 1, 2). There are some ƒ/0.95 lenses, such as the Canon 50mm ƒ/0.95, Leica Noctilux 50mm f/0.95 ASPH. Beyond that, expect no better than ƒ/1.2 or so.

While the superfast lenses of ƒ/0.95 – ƒ/1.2 are renowned for their beautiful shallow depth of field, you can still use them to photograph subjects at the hyperfocal distance as noted earlier.


Note: It is possible to have a lens faster than ƒ/0.5, but it won't have a combined light transmission (i.e. T-stop) faster than T/0.5. That is, the real light loss of the lens, given by its transmission ratio (less than 1, around 0.7–0.8 for uncoated lenses; upwards of 0.96 for lenses with antifreflective coatings), can be modeled as an ideal lossless lens with a fixed neutral-density filter built-in. The combination of geometric aperture (represented by ƒ-number) and built-in "ND filter loss" characteristic (T-stop) will never be less than 0.5. The reason for this is because ƒ-number N is really a consequence of the lens's numerical aperture,

N = 1 / 1/(2×sin(𝛼/2))

where 𝛼 is the acceptance angle of the optical system. The maximum value of the sine function is 1, which happens when its argument is 90º. This doesn't say the every, or perhaps even any optical system can have an acceptance angle of 180º, this just puts a hard upper limit on the numerical aperture, and thus, a maximum "speed" on any optical system.

When I said the maximum T-number of the lens system was 0.5, implicit in that is the assumption that we're talking about an image-forming optical system. That is, we're interested in photographs, sharp images with low or minimal aberrations, distortions, etc. It is possible to have ƒ-numbers somewhat lower than 0.5, but the system is no longer usefully image-forming. This comes back to the étendue-conserving "you can't squoosh light onto a smaller area" XCKD What If? explainer.

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  • You can't get more than the source is generating/reflecting (which is why you can't light a fire w/ moonlight). But you can get w/in several magnitudes (~1 stop), which is why you can light a fire with direct sunlight. IDK how they hyperfocus technique has anything to do with camera/lens design. Jul 13 at 12:53
  • Hyperfocus technique has nothing to do with lens design. OP asked for both deep DoF and fast lens. So I addressed hyperfocal distance as a way to maximize DoF.
    – scottbb
    Jul 13 at 12:55
  • @scottbb I think you may have misunderstood what I meant by "within a couple of orders of magnitude of the brightness of direct sunlight". On a clear day I measure about 300,000 lux in direct sunlight. In my question I meant that I was hoping to get around 3,000 - 30,000 lux of light falling on my film at the brightest points on the image. I think this is possible without a Jupiter sized lens, because I already fashioned a small makeshift camera, exposed it for 4 days, and saw some (minimal but noticeable) lightening of my homemade film. Still, your answer is the best so far. Jul 13 at 18:23
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    @BenHershey Ah, indeed, I did misunderstand that. I'll edit that. Thanks. =)
    – scottbb
    Jul 13 at 18:29
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    @StevenKersting 1. Unless specifically subscripted or otherwise caveated, I always assume "orders of magnitude" (OOMs) to be base-10. Thus, 3 stops (base-2 OOMs) is a factor of 8, or very roughly 1 "typical" OOM. I use "stops" photographically, and "bits" in computing and information theory for base-2 OOMs.
    – scottbb
    Jul 14 at 16:17
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No. The aperture number determines the ratio between light emitted and light captured. The more light you capture, the more angles of the emitted light you need to catch and different angles only converge in the focusing plane. You can warp the focusing plane to better fit the subject (full-frame cameras and tilt-shift lenses do this), but the more light you capture from the focusing plane, the faster the "viewing rays" range diverges as you move from the focusing plane.

And for the kind of exposure duration you are talking of, plants are likely to object to extra-bright illumination. You can do some extra "natural" illumination by working with reflectors.

And if the reflection is not nearly diffuse, you can make the most of your light by trying to capture the angle where the reflection is strongest. However, that appears to be tricky to implement for hour-long exposure times using sun light. You would need to find some arrangement where the glare wanders across the image in a manner where it covers most of your area of interest in the course of exposure: that would allow you to squeeze out some exposure beyond what the aperture would deliver assuming an idealised matte reflection.

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Depending upon what you are shooting, there is a way to cheat to get an apparent deep depth of field and bright image. Tilting either the lens or the image plane can align the focus to a plane other than the typical perpendicular.

From www.australianlight.com :

Normal Perpendicular image plane

Normal

Tilted Image Plane

Tilted

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Is it optically possible for a custom-built camera to form an image with both a reasonably deep depth of field and a very bright image (lots of light gathering)? Is it simply a matter of lens shape and size and camera body dimensions?

There are three ways that can be done.

Firstly, you can improve sensor technology. For example, moving from a film camera to a digital camera increases the quantum efficiency of the sensor/film. The trouble is, the quantum efficiency cannot exceed 100%, and we have already such good quantum efficiency that major improvements are not possible due to the 100% limit.

Note nearly any decent sensor allows a ridiculously high ISO -- this increases noise, and this may not be what you want.

Some ways that are possible are a black-and-white sensor (so light doesn't get lost because it's incorrect color for the pixel), and cooling the sensor to cryogenic temperatures to reduce thermal noise.

Secondly, increase the exposure time. However, this only works with objects that don't move (although with image stacking you can correct this in post processing, and that's the way many pretty astrophotography images are made).

Thirdly, add more light to the scene. Flashes do that and nearly every good camera has a flash hotshoe. This is the most practical way for most purposes. However, it only works well if photographing something that's reasonably near. Don't try using flash with landscape photography!

What doesn't work is moving to a bigger sensor camera, as bigger sensors are usually associated with shallow depth of field and correcting the depth of field by increasing aperture F-number eliminates any gains you make in light gathering ability.

For your use case, it seems the best is to not do what you're doing but rather use a better sensor. Flashes usually can't overpower direct sunlight and if your sensor is so poor that it requires minutes of exposure, selecting a better sensor, something more like real film would help.

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  • There is one way you miss, adding special lens which offer huge depth of field Jul 11 at 20:01
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    @BenHershey, the lens I talk about is tilt-shift. Jul 12 at 4:34
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    @RomeoNinov front tilt offers control over plane of focus orientation and therefore provides spatial control over the orientation of depth of field. There is no silver bullet. At wide apertures there is shallower depth of field with a tilted lens and more depth of field at narrow apertures. Some scenes may have geometry that lends itself to an alternate plane of focus. Not all scenes do. Jul 12 at 17:46
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    @BobMacaroniMcStevens, yes, but this is good option to be considered :) Jul 12 at 17:57
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    @Romeo Ninov thank you. Yes, this is helpful information. Doesn't increase depth of field per se, but makes a shallow depth of field more workable and so I consider it helpful to my question. Upvote. Jul 13 at 18:13
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You can't have a small aperture (hence deep field) AND a bright image. What you CAN do is make a less bright image more useful by choosing a faster film or more sensitive sensor.

More sensitivity traditionally means less quality. But - unlike the aperture/depth of field equivalence - this is not a Law of Physics. Technical improvements can be (and constantly are) made.

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The simple way to solve the narrow aperture slow film problem is with studio strobes.

Multiple flashes may be required for a single exposure since “A couple of orders of magnitude” is about six or seven stops of light. But with long exposure strobes can be fired manually at your leisure.

Strobes will also provide greater lighting design possibilities than a special lens and/or camera.

This seems to be a solved problem presented in XY problem form. The practical solution exists off the shelf. The market is efficient here.

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Optical geometry and optical physics are also part of how cameras are built. There is unfortunately no magic trick to focus more light energy on sensors in addition to play with aperture (which must be small in your case), time exposure and sensitivity of your sensor.

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A significant factor of depth of field that hasn't been mentioned yet is magnification. And since you haven't stated what you want to take pictures of, it's worth noting.

The aperture's physical size is what controls the amount of detail blur (diffraction) and depth of focus (relative sharpness at image plane); but that is not the lens' f#, effective aperture, entrance pupil size, nor depth of field (apparent relative sharpness in output image).

The entrance pupil, which is what controls the exposure, is the aperture's physical size as seen/magnified by the objective elements before it. What can happen is that the lens' magnification is changed and that simultaneously changes the magnification of the aperture... that is (basically) how a constant f# zoom lens works. Or the lens' magnification can be changed w/o a simultaneous/equal change in the magnification of the aperture opening, resulting in a variable f# zoom lens. So you can manipulate the magnification to manipulate the exposure.

The magnification also makes the diffraction/sharpness/lack of sharpness more apparent. E.g. lower magnification lenses have greater DOF w/ the same physical aperture diameter (lower f#). And this is why smaller image areas/sensor generate greater DOF; because they use a lens of less magnification to record the same scene.

And similarly magnifying the image output (larger sizes/shorter viewing distances) also changes the depth of field. If you display/present your image smaller it will appear sharper with greater depth of field.

And you can use reduced magnification to make a lens' image circle smaller. That will increase the depth of focus, the resulting depth of field, and light density. E.g. you could design your custom camera to use a large format lens with a large image circle, and lenses between it and the image plane that reduces that circle to a smaller size for a significant increase in exposure/light density/DOF. Just reducing a 35mm image circle down to APS size would double the exposure/light density and increase the DOF by 25% (one stop).


Edit to add/clarify:

An f/1 lens with no transmission losses (t/1) means there is no light loss relative to the light that is incident to (falling on) the objective element/lens. And it would be a 100% exposure (image illuminance) when the projected image circle/area is the same size as the objective element. I.e. a 43mm objective t/1 lens exposing a 35mm sensor area (43mm diagonal) is image illuminance exactly equal to the intensity of the light falling at that location... i.e. the same magnitude as direct sunlight.

However, there are always transmission losses; an f/0.7 lens with 50% transmission loss would be a t/1 lens.

Many lenses are actually concentrating the objective area into a smaller image circle, which increases the density/illuminance. So, if you have an f/1.4 lens with a 60mm diameter objective projecting a 35mm image circle, it is again image illuminance exactly equal to direct sunlight illuminance (1 stop larger diameter collected w/ 1 stop transmission loss).

Similarly, if you took a 100mm f/2.8 lens with a 120mm image circle (Zeiss Planar designed for MF), and concentrate that down to APS size (30mm diagonal) using negative magnification, the resulting image illuminance would be equivalent to ~ f/0.7... slightly greater than the intensity of the light collected. While at the same time the resulting image would still be 100/2.8 in terms of FOV/DOF (4 stops greater DOF than the f/0.7 illuminance).

And, if you concentrate a large enough image circle into a small enough image area, you can far exceed the illuminance of direct sunlight (e.g. start a fire)... That is still many magnitudes away from the intensity of the sun itself, but that is not the issue in question.

This is all just what is known as bellows factor, a common issue in macro photography. If you make the image circle larger (extending the bellows) it results in a reduced exposure due to light spread (inverse square law), and causes a reduced DOF in the output image (because the image circle is then being cropped, and therefore what remains is magnified more for any given output size). And the opposite is also true if you reduce the size of the image circle (given the image circle is larger than the image area).


So, yes... you could design a custom camera that would increase your ability to record a sufficiently bright image with acceptable/desired depth of field using chlorophyl; I just can't say what that image would be of (magnification/field of view).

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