Let us begin by listing a few of the common myths and wives' tales regarding "flat-field" lenses.
How many of you have been told that you shouldn't photograph three dimensional objects in the studio with such a lens? How about the admonition that flat-field lenses are not good at infinity or for landscapes? In a related subject, have you been told that in order to photograph a group of people it is necessary to place them in a semicircle so that they will all be in focus? Every one of these statements is bunk, and using a little theory, we will explain why. We will also explain how to use such a "tricky" lens.
Actually, there is absolutely no trick to it at all. First, a few definitions. By specifying a flat-field lens, we imply that there are lenses which do not have flat fields. This is very odd, you might say, considering that film planes are flat surfaces. In fact, film planes over the last century, with very few exceptions, have been flat! How, then, would one use a "curved-field" lens? At this point, it is tempting to state categorically that all normal photographic lenses have flat fields, but that is too simple an explanation.
Where did the term "flat-field lens" come from, and what is such a lens. The term probably came from the graphic arts field, where highly corrected and usually apochromatic lenses are used to copy, reduce and enlarge flat objects to flat films. Because of the rigorous dimensional requirements of four color process work, and to a lessor extent, line and text reproduction, these lenses had to function within very strict parameters. This included not only field flatness, but distortion and secondary spectrum.
But wait a minute. We just pointed out that regular still cameras also have flat films. How does this differ from process cameras? Don't I also want a high degree of image flatness in my camera? The answer is yes, but with some explanation.
And now a little theory. It is unquestionably the goal of the lens designer to design every lens with as flat a field as possible, for the very fact that all but special cameras have flat image planes. But therein lies the problem. Designing a lens with a flat field is not so simple.
A simple lens (I like to call it a "natural" lens) does not have a flat field. A very good example of this is the eye. In imaging a flat subject such as a wall, the axial distance from lens to subject is not the same as any oblique distance to the subject. Thus, the image would naturally be formed on a curved surface such as the retina. It is the designers job, through the judicious use of different glasses, curvatures and astigmatism to make the field as flat as possible.
The natural, uncorrected curvature of the field of any lens is described mathematically by a value known as the Petzval Sum. Originally quantified by Joseph Petzval of Petzval Portrait Lens fame in the latter 1800s, the Petzval sum is the sum and product of the lens element powers and refractive indices of the glasses. In simple terms, for a simple thin lens of one diopter power and made of glass having an index of 1.50, the Petzval sum would be (Kingslake, 1989):
1/1.5=.666
From the above expression, it can be seen that the higher the refractive index or the lower the power of the lens, the lower the Petzval sum. Remember, the diopter power of a lens is the inverse of its focal length in meters. Therefore, a lens of .5 diopter would have a focal length of 2000mm, and a Petzval Sum of .33..
The lower the Petzval Sum, the lower will be the curvature of the image surface, as you will see from the formula for displacement from the theoretical film plane, or Gaussian Plane (Ray, 1988):
y2 P ____ d= 2
where y is the image height (off axis distance) and P is the Petzval sum. All of the above is very simplified and deals only with a single element lens.
It was discussed in a previous series of articles that the structure of a camera lens image is actually that of two images, those of the saggital and tangential images. In considering a small field, a lens would be completely astigmatism free if pure field curvature is allowed to exist, such that the saggital and tangential image surfaces are coincident with the Petzval surface.
By choosing appropriate glasses and indices which could help to reduce the Petzval Sum, and by allowing certain degrees of astigmatism, the compromise of a flat field may be achieved. In this case, the distance between the astigmatic surfaces is the degree of astigmatism for that point in the field. Midway between the two surfaces will be a circular or near circular patch, or circle of confusion. The greater distance between the surfaces, the larger the circle of confusion. By definition, it is not possible to correct field curvature and astigmatism simultaneously. Thus, If a lower amount of astigmatism is desired, some amount of field curvature may be reintroduced.
For wider fields, negative or over corrected astigmatism is introduced which may cause the tangential surface to be behind the Gaussian plane. At some point, due to high order astigmatism there will probably be a reversal in one or both astigmatic surfaces such that they cross, forming a node (Cox, 1974). The precise topography of these surfaces, as has been pointed out, depend upon the combination of Petzval Sum and Astigmatic corrections, resulting in the desirable compromise, such that the image surfaces come as close as possible to the Gaussian plane.
All of this should illustrate to you that field flatness is a matter of degree. As a practical matter, all modern lenses and many classic lenses are extremely well corrected in this regard. The degree of field flatness and astigmatic correction is also dependent upon field of view. Because all of the image surfaces will coincide on axis, and diverge from that point, a higher level of both field flatness and astigmatic correction may be achieved if the lens is corrected for a smaller field. For this reason, process lenses have traditionally been lenses covering only about 40 to 45 degrees. Within this field of view, it has been possible to correct astigmatism and achieve a flat field to very high standards. Normally made in apertures of f/11 for long lenses and f/9 for shorter ones, the classic 45 degree process lens the Apo Artar, is extremely well corrected and may be used wide open, although most process work is done at f/16 or f/22.
In correcting so called wide field process lenses, such as the Schneider G-Claron it is obvious that the most important consideration would be field flatness and astigmatism. As we have seen, the two are inseparable. We have only discussed the issue of the shape of the field, and ignored other aberrations. If the designer is free to sacrifice to some degree the correction of other aberrations, the field flatness can be further perfected and a wider field may then be dealt with. Since process work is generally done at small stops, the designer knows that he can make field flatness correction at the expense of aperture sensitive aberrations, principally spherical aberation and oblique spherical aberation. At apertures wider than f/16 the higher order aberrations have a significant effect on lens performance. Since wide fields also involve higher order aberrations, by limiting the aperture, the correction of these aberrations may be dealt with on a field angle basis with greater ease (Cox, 1973).
The result, of course, is a wide field lens whose widest aperture is limited to f/9. Except for possible portrait applications, the lens should not be used wide open due to some residual spherical aberation. However, stopped down to f/16 or f/22, the lens is an excellent general purpose lens, and may be considered diffraction limited at the latter stop.
Now that we have described in some detail the character of field flatness and how it is achieved, we may assume for the sake of argument that all lenses have a flat field. Using the process camera as a model, let us examine what happens at a magnification of 1:1. At the easel, or copy board, the subject is a flat object. On the film side, the lens must project a flat, undistorted, identical rendition of the object. Due to the corrections, astigmatic and otherwise, such is the case, with very great accuracy. Now conduct the same model at a magnification of 2:1. Again, the image cast upon the film is a near perfect representation, to scale.
If we take this model still further, to a ratio of 10:1, such that the image is one tenth the size of the object, we will still find near perfect reproduction of the object. There may be the slight beginnings of certain aberrations which are dependent upon symmetry. These are coma, lateral color and distortion. Since process lenses are usually symmetrical, and usually corrected absolutely only at equal conjugates (1:l), the further one departs from these conditions, the more one will encounter the symmetrically dependent aberrations. In real terms, however these trace aberrations are usually quite insignificant. Remember, for instance, that the Dagor and the majority of its relatives of the early part of this century, and well into the sixties, are actually completely symmetrical lenses, and should technically only perform optimally at 1:1. In fact, I have had excellent 2x enlargements of my 8x10 negatives using a Dagor at f:16. Yet, as we all know, these lenses have been used routinely at all distances and for all purposes for years, and have performed well. At normal working apertures, any residual aberrations due to asymmetrical working conditions are negated by medium to small stops.
To take our model to the extreme, we may regard infinity as an infinitely distant flat plane. Any subject at infinity therefore, will still be rendered by any properly corrected lens as a flat image at the film plane. In a modern lens plasmat corrected for 1:20 (as most of them are), this image will be quite sharp even at f:5.6, and will not suffer the same degree of trace symmetrically-dependent aberrations as will a Dagor or G-Claron at their widest apertures. However, at f/22, the difference between all of the above lenses will be very hard to tell, as they will all be virtually diffraction limited at this stop. The worst of them will most likely be the Dagor which does not have as flat a field as either the G-Claron or the modern f/5.6 Plasmat. Those of you who use Dagors know that I'm splitting hairs here.
Please notice that we have shown that it is highly desirable to use a lens with as flat a field as possible. This would be especially important at infinity, at which distance the depth of focus(the "tolerance" at the film plane) is most critical. Where the nonsense about not using a "flat field" lens at infinity came from I just don't, unless it was confusion with other aberrations corrected at 1:1.
To return to our 10:1 model which might also represent the working distance in a studio, I reiterate that a properly corrected lens will give both flat object and image planes. That one would in some way be hindered by using such a lens to photograph furniture or any other three dimensional object in the studio is quite unsupportable. Such objects would generally require significant stopping down in any case, and the degree of field flatness is probably less significant than if one were to photograph some plane object, were simple Shiempflug manipulations would do most of the job.
Likewise, regardless of what working distance, a row of people simply represents a flat subject which would be reproduced as a flat image, just as in the other examples. There is absolutely no reason to form the people in a semicircle in order to bring them all into focus, as some writers have claimed.
Many of us have used the narrow field process lenses such as Apo Artars and Apo Ronars as long focus lenses for years with excellent results, and due to their generally slower apertures, they tend to be nice and small compared to their focal lengths. More recently the G-Claron and Fuji AS lenses have come into use, both as long 4x5 lenses and as wide field 8x10 lenses, in both cases offering the advantage of light weight, and also with excellent results. In the case of the former lenses, there are no detectable aberrations when used at infinity even wide open. As one would expect after our discussion, the latter lenses should be stopped down two to three stops for use at infinity.
In closing, I would like to say that I object to the term "flat-field" lens. It is the fervent goal of the designer to be sure that every lens has as flat a field as possible. Therefore, we should agree to call all lenses (particularly modern lenses) "flat-field" lenses, or with the knowledge that Petzval sums and astigmatic surface corrections are a matter of degrees and not absolutes, we should agree that no lens has a flat field. I prefer to speak in terms of degrees, but even so, there should be no question that the flatter the better.