Focus of lens dropoff from center to ends [duplicate]

Question

I have come across a couple lens manufacturers that mention that when a lens is focused such that the center of the FOV is well focused, the extreme ends of the FOV will be slightly defocused.

What is the reason for this? I was of the opinion that lenses are focused for a certain distance and if the entire FOV is filled with a target at that distance, it would be equally well focused all over.

Thank you.

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edit: after going through some more I came across the page where they measure resolution of lens. It seems like they focus at the center (which reduces the resolution at the sides since it is in relative defocus). And then they turn back the focus some so that it defocus the center a bit for larger gains in focus at the ends. Is this common practice?

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edit: for instance, this is an excerpt from this page on Edmund Optics

This also can cause issues depending on whether the system is only focused in the center of the FOV or across the entire FOV; because of the resolution varying based on location, it can be difficult to determine when the entire FOV is in best focus. Some lenses obtain very high resolution in the center of the FOV, but very low resolution in the corners when the lens and camera system is focused on the center of the image. A slight defocusing of the lens can balance the resolution across the field, although usually to the detriment of the center resolution.

Answer 1

The issue you're describing is usually related to field curvature and how a lens attempts to correct for it.

A simple theoretical thin lens has a field of focus that is a portion of a sphere the size of the focus distance (the distance between the camera and the subject that is in focus). Most modern lenses have multiple elements that attempt, more or less successfully, to correct for field curvature and other optical aberrations demonstrated by uncorrected simple lenses.

All lenses have field curvature until they're corrected for it to one degree or another. There is no refractive lens with a theoretically flat field of focus. The fact that most modern lenses get close enough that we don't notice doesn't mean lenses inherently have a flat field of focus, it just means we're getting pretty good at making lenses that look like they do.

The goal is a flat plane of focus, but this is rarely if ever achieved to the degree that variations in the shape of a lens' field of focus cannot be measured. The shape of the field of focus of many highly corrected lenses is more like that of a wavy lasagna noodle than a flat plate.

The purpose for which a lens is intended will influence the decisions made by the designers as to how they wish to approach the lens' field of focus.

• Macro lenses (true macro lenses are usually prime lenses with at least a 1:1 reproduction ratio) tend to be designed to have the flattest field at the lens' minimum focus distance (MFD).
• Telephoto lenses tend to attempt to have their flattest field of focus at very long focus distances.
• Some lenses intended primarily for use making portraits leave some (or all) of the field curvature uncorrected. These lenses give a different "look" that highly corrected lenses do.
• Most zoom lenses include design compromises that can vary across the lens' focal length range. This includes corrections for all of the main optical aberrations including field curvature.

Answer 2

It is called Curvature of Field (Google it). A lens focused at 20 feet is focused on a spherical surface with radius of 20 feet. Also a focal length of 50 mm is focused on a spherical surface with radius of 50 mm (affecting focus at frame corners). There are corrections possible to flatten the field more, but not always perfect.

Answer 3

To explain, you need to envision that the visa you are about to photograph, is comprised of zillions of tiny points. Each point is a reflector of light (or light source). An imaginary line can be trace from each point through the lens to the surface of film or digital sensor. Each point on the vista will have a corresponding point imaged on this surface. By the way, this is a reasonably accurate description of what is actually happening. Examining a ray trace of the light rays that make up the image of any point, the rays trace out the shape of a cone. The apex of this cone just kisses the surface. Should the apex not kiss the surface, the image of the tiny object point will be too big. To be declared tack sharp, the image of the object point must be no larger than ½ mm in diameter when viewed at standard reading distance. Because modern cameras produce miniature images that must be enlarged to be viewed on computer screen or as a print on paper. Thus the lens maker presupposes that the degree of enlargement will be about 10X for a full frame camera FX and about 15X for a compact digital DX. That requires that the diameter of this image point be 0.05mm for the FX and 0.03mm for the DX. By the way, this circle is called the circle of confusion because it has indistinct boundaries and it is jumbled by touching adjacent circles.

Now the camera lens images a 3D world and projects that image on a flat surface. Only the center portion of that image is photographically useful. This area is called the circle of good definition. The areas outside this area will be distorted and dim. The camera sports a mask and baffles that crop the projected image to the dimensions of the format size.

Now to answer your question: The circles of confusion are always indistinct because every lens has unresolved aberrations. Now imagine you are a bug waking on the surface of film or digital chip, looking back at the lens when the picture is taken. If you are in the center of format, you see the lens as an illuminated circle. When you walk to the boundaries of the format, you see the lens as an ellipse. Now an ellipse has less surface area than a circle. Thus the image the lens projects at the edges will be dimmer. Also, the light from the lens is coming in at an angle. The apex of the cone, as it hits the film or digital sensor is also elliptical. This shape will not appear a sharp as a circle (called cosign error).

This only partially explains why the edges of a projected image are not tack sharp. Perhaps, if you study optics, you may be the one that creates a lens that deliverers what we all want, “a faithful image”.