Should lenses of equal quality for smaller sensors be cheaper?

Question

In theory do we expect lenses of identical specs and quality to be cheaper when designed for smaller sensors? My expectation is that the answer is yes, because all of the things that lenses struggle to control — chromatic aberration, vignetting, distortion, etc. — are exposed over a smaller central region. Or, put another way, if you take a full-frame image and center crop it you always end up with less of these bad things. I'm also thinking of the exit image quality problem as sort of an inverse of the entry image problem, and we know that larger apertures are optically more difficult.

Now what about in practice: Is the answer different? For example, it could be "yes" in theory and "no" in practice because everyone designs and builds to full-frame specs anyway, and economies of scale cancel out whatever theoretical savings there might be for lenses designed for smaller sensors.

Update: Some of the answers so far assume that the complexity of the lens must be constant, and thus only address the marginal cost of reducing the size. Obviously size/material savings are not going to be significant when talking about tradeoffs like this in quality glass.

I was thinking more along the lines of being able to reduce the quality and maybe even number of the lens components. Again, because I have a hard time visualizing the optics of the exit cone I hope the engineering is roughly analogous to the input side of the lens: We know that a high-quality large-aperture lens faces the biggest challenges shooting wide open because it has to take incident light and bend it through more extreme angles without introducing chromatic aberration, distortion, etc. If you're willing to shoot a prime at, say, f/10+ then a lot of those challenges go away. So I'm assuming that on the exit side it's somewhat similar: the larger the circle the more you have to work the optics to keep quality constant edge-to-edge. Just as closing the aperture relieves you of challenges in maintaining quality, doesn't reducing the angle of the exit cone we care about by reducing the sensor size make preserving quality across the sensor easier?

Another Update: Let us assume that we're talking about sensors with the same pixel pitch and technology. I.e., we aren't asking the lenses for smaller sensors to compensate for any shortcomings that often accompany reduced sensor size. Though, again, I assume that in practice "good" glass is generally running close to the upper (diffraction) limit of resolution.

Answer 1

Smaller format lenses are eased by having lower maximum image heights and smaller fields of view at the same focal length. Each aberration has explicit field dependencies which describe the rate at which they grow. For the following equations, y is the ray height at the lens and h is image height.

Spherical Aberration varies by y³.

Coma varies by y²h.

Astigmatism varies by yh².

Field Curvature varies by yh².

Distortion varies by h³.

(sourced from Modern Lens Design or Modern Optical Engineering by W.J Smith)

If you hold field of view constant and merely reduce the lens size proportionally to the reduction in sensor size, then optical performance actually improves. For instance if you had a plano-convex singlet of focal length 100mm and you scaled it to 50mm, the curvature of the front surface would be twice as strong as before, the back focus would be twice as short, and the diameter would be half what it was originally. Typically a stronger curvature, and in this case the reduced diameter coupled with the reduced image height, is always superior.

Therefore, if you want to hold performance constant then as you reduce the lens size you may choose less expensive lens designs with lower "base" performance.

Answer 2

It's only the image circle that changes, really. Everything else either remains the same or becomes a bigger problem (for instance, the need for even wider apertures for the same depth of field at the same angle of view and subject distance means that greater degrees of correction will be required for things like coma, spherical and chromatic aberration). (A 40mm f/0.85 lens for Micro Four Thirds -- which exists, and costs $2000 -- is the functional equivalent of a $500 85mm f/1.8 on 35mm "full frame", or almost, since it's a little slower.) The largest elements of the lens have to remain the same, and you don't gain a whole lot of cost savings reducing the image circle -- it's not zero savings; it's just not as much as you might think, especially when the difference between sensor sizes isn't huge. And that savings will be applied to the dubious "feature" of putting back the vignetting you lost not using a lens with a larger image circle.

On the other hand, lenses of lesser quality might not display quite so many problems on a smaller sensor, so in that sense lenses for smaller sensors can be cheaper. (Imagine what the barrel distortion of an APS-C 18-to-whatever lens would look like on a full frame sensor.)

Answer 3

For Canon, the EF-S was designed to precicely scale down the geometry of EF by the crop factor. SO, the EF-S 17-55 f/2.8 gets its design kick-started by shrinking down the existing design for ... well, they don't make a EF 27-88, so not the clearest example. But I have read that some designs are scaled down.

IAC, the rather large 17-55 is 1.6× smaller in every direction (diameter and length) as the equivilent fov and speed on a Full Frame lens, and the volume of glass is 1.6³× lighter or one quarter the weight! Now in reality the bulk of the diameter of the finished lens will include motors and trackways and gears that won't scale down by the same factor, and the glass proper is not the full weight of the lens.

But since "glass costs", I would certainly expect it to be cheaper than the equivilent fov and f-stop in a larger form factor.

There are other factors that preclude exact comparisons though. There are no L-series made for EFS. but, the afore mentioned fast wide zoom is reportedly very good, just about "L" quality for the glass, just not in overall build quality, environmental sealing, and ruggedness. That means it was much cheaper than the equivilent supposing I don't need those in-the-field pro features.

In particular, wide angle is easier on the smaller form factor, and paying for quality in the non-existent corners is a waste; especially when shorter focal lengths are needed for the same fov. A scaled-down realistic fov lens is far more efficient than a full-frame extreme-wide lens, since "wide" is where things start getting expensive.

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In short, I expect zooms that are shorter than about 35mm focal length to be significantly cheaper in a crop-specific version, and that is magnified for fast lenses too.

Where wide-angle fov gets awkward, and the needed focal length is awkward on a full-frame but OK on a crop body, big difference.

Answer 4

This part of my answer is under the assumption that you mean a 'cheaper' price to the customer. See the bottom for my response developed under the assumption that you mean 'cheaper' to build.

Price of any product, including a camera lens, is based on what the market can bear. The cost to produce a product is merely one element that determines a price. Let's say a manufacturing CEO has found that she can produce a successful and popular product at a lower cost than she had previously. Will she lower the price? Most of the time, her decision will be "no". People are comfortable paying that price already, the extra profit she will make can be invested into R&D, or given to the hard working engineers as a raise they so deserve.

It's the competition that will drive prices down. (Which is why I am enthusiastic of any camera brand that innovates and drives competition).

When our CEO wants to gain market share for a product, she may lower pricing as one option to encroach on her competition's market share. That decision may be made regardless of the price of a particular product. On the other hand, that decision may drive the CEO to source or build the product with cheaper components to undercut her competition.

So, you can see, a price of a product is only related to its cost in as much you want to be profitable.

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Incase you mean 'lower cost to build', then here is my response - If a lens manufacturer were selling lenses with the same magnitude as someone selling cans of soda or other typical commodity consumer good products, then you would probably see economy of scale that a small material reduction will be noticeable on a corporate sheet. However, for companyies that are only selling tens of thousands of a particular lens, then there isn't much saving by slightly reducing the size of the lense. Perhaps just a few dollars per lens. On the other hand, the same diligent factory employees have to be involved, the same infrastructure is used to make the lens, the same Non-Recurring Engineering time is necessary to design the lens, and the same management structure is there, too. So the raw material cost was just a very small part of the overall cost of goods sold.

So, bottom line, No. Not much cheaper in practice.

Answer 5

If you mean cheaper to produce, then yes. But maybe only slightly so as there are many things besides material cost that contribute to the production cost of a lens. A lens designed to throw a smaller image circle has a few advantages:

• It needs to collect less total light to create the same field density of light on a smaller sensor. This allows a smaller entrance pupil, often referred to as effective aperture, for the same f-number and exposure value.
• It requires a shorter focal length to create the same field of view on a smaller sensor than what is required for a larger sensor. This also allows a smaller entrance pupil, often referred to as effective aperture, for the same f-number and exposure value.

The most expensive material in most lenses is the corrector lens that is usually (but not always) found as the rear element of the front group. Since the front group is what can be most significantly made smaller for a lens designed to work with a smaller sensor there is a cost savings in terms of the amount of exotic materials needed for the corrector lens. But this might not be a significant portion of the total cost to produce the lens.

Answer 6

It depends on what you mean by equal quality. A smaller sensor requires less light to be focused on the sensor as the sensor is much smaller, so much smaller lenses can be used while maintaining a roughly equivalent level of resolution on the sensor, but they also gathered far less light, and thus less information as well.

The sensor itself is more limited due to the size. We can discard the excess parts of the lens that wouldn't be used by the sensor, but we are still stuck with all the limitations of the sensor. We could try to compensate for some of the limitations of the sensor by improving the quality of the lens substantially to try to cram in as much information as we would capture with a larger sensor, but this would drastically increase the cost of the lens (and isn't fully possible because of issues like diffraction limiting.)

So the answer is yes and no, a lens with the same overall optical resolution properties that only has to resolve a smaller area is cheaper, but resolving the same amount of detail in a smaller area would likely be close to the same cost or even possibly more expensive.