Autofocus Accuracy Specifications in Canon EOS Digital SLR Cameras

Transcription

1 Auto Accuracy Speciications in Canon EOS Digital SLR Cameras Douglas A. Kerr, P.E. Issue 1 June 6, 2005 ABSTRACT Canon, Inc. typically epresses the accuracy tolerance o the auto system in their EOS digital SLR cameras as a raction o the depth o. O interest in relating this speciication to its impact on actual photographic work is how this relates to depth o ield. In this article, we describe that relationship, as well as the basic signiicance o the speciication, and o itsel. ITRODUCTIO Canon, Inc. usually states, in the published speciications or their various digital single-lens rele (SLR) cameras, an accuracy tolerance or the auto (A) system in terms o a raction o the depth o o the camera. Oten, or the basic A mode, that speciication is within the depth o. or the high precision A mode that applies in certain circumstances, that speciication is oten within 1/3 the depth o. Oten, users ask, Isn t that the same as within the depth o ield (or within 1/3 the depth o ield )? Usually the response is, Certainly not those are two vastly dierent quantities. But in act the answer isn t quite that simple. In any case, it is diicult or a photographer to relate an A accuracy epressed in terms o the depth o to its impact on practical photographic work. 1 Typically, the photographer may wonder whether she can epect, when ing on an object, that the actual setting produced by the A system will be close enough to the object distance that the object will be within the depth o ield or that situation that is, whether she can epect the, despite the A error, to still be in adequately sharp. In this article, we will eamine the relationship between A accuracy speciications epressed in term o and the implications o those speciications in terms o ield. DEPTH O OCUS Depth o is ordinarily deined in this way. Imagine a camera aimed at a test object at a certain distance. The lens generates a ly-ed o a test object at a particular distance behind the lens (hopeully, at the location o the ilm 1 As an actual distance, the depth o is perhaps only ±0.04 mm!

2 Auto Accuracy Speciications Page 2 or digital sensor). We then ask this question: at what range o distances behind the lens is an produced that, while not ly ed, may still be considered adequately sharp? That range o distances is deined as the depth o or the particular situation. O course, or this to be meaningul we must have a quantitative deinition o what constitutes adequately sharp. As in the case o ield, we do this by stating that an will be considered adequately sharp i the circle o conusion (blur circle) produced in the imly-ed rom a point on the object does not have a diameter greater than some value we arbitrarily adopt (the circle o conusion diameter limit, or DL). This deinition o has classically been related to the question, with the lens properly ed, how ar can the ilm be displaced rom its intended position and still have the adequately sharp. We see this concept o in igure 1. ote that the DL used there is unrealistically large so as to make the depth o large enough or a convenient illustration. (a) (b) DL g (c) g h h Depth o igure 1. Depth o

3 Auto Accuracy Speciications Page 3 The red lines in the igure show the convergence o the outermost rays originating at a point on the object. In Part (a), we see the lens properly ed on some object, such that a ly ed o the object is ormed on the sensor, at location, presumably the intended location o the sensor. In Part (b), we move the sensor orward to point g. There, a blurred is ormed, one whose circle o conusion has just the diameter we established as our circle o conusion diameter limit (DL), our criterion o acceptable sharpness. In Part (c), we move the sensor backward to point h. There. we also have a blurred, again one whose circle o conusion has the diameter o our DL. The depth o in this situation is said to etend rom point to point g. The other depth o deinition There is also a second, subtly dierent, deinition o. This time, imagine the ly ed o a test object alling precisely on the sensor. Then consider shiting the setting o the lens so as to move the ly ed orward and back. We ask the question: or what range o distances to the ly ed is the on the sensor itsel still adequately sharp? or all cases o interest, the numerical results o these two deinitions will be almost identical. But it is important to recognize the conceptual dierence between them. Otherwise, some o the story won t seem quite right. In particular, it is really this second deinition that directly relates to the speciication o A error in terms o. Here, we don t have an error in the position o the sensor, with the ormed where the sensor is supposed to be. Rather, we have an error in lens setting such that the ly ed is created closer to the lens, or arther rom it, than the location o the sensor. We see this concept o in igure 2. As beore, in Part (a) we see the lens properly ed on some object, such that a ly ed is ormed on the sensor, at location, presumably the intended location o the sensor. In Part (b), due to an error in the A system, the lens is not ed on the object but in act at a greater distance. We see this by noting the indicator on the lens scale at a position arther toward the ar direction than in Part (a). As a result o this mis, the ly-ed o the object is ormed not at the sensor but at location k (or it would be i the sensor were not in the way!). At the sensor, a blurred is ormed, one whose circle o conusion has the diameter o our DL. Thus the on the sensor just barely satisies our criterion o acceptable.

4 Auto Accuracy Speciications Page 4 (a) (b) k DL h (c) g, h: limits rom irst deinition j g j k Depth o igure 2. Depth o (deinition 2) In Part (c), we see a situation in which the lens has (through A error) been ed at a distance closer than the object. In this case, the ly-ed o the object is ormed at location j, in ront o the sensor. Again, the on the sensor is blurred, with a circle o conusion whose diameter is just that o our DL, an that just barely satisies our criterion o acceptable sharpness. Under deinition 2, the depth o o this system is said to etend rom location j to location k. On this igure we have also shown locations g and h, the limits o the depth o in this situation under deinition 1. ote that they are not quite the same as the limits o under deinition 2 (locations j and k). O course, as mentioned previously, we have shown depth o or an etremely large DL. With a DL in the range usually used, the dierence between the limits or the two deinitions o would be negligible. How big is it, anyway? Oten (under either deinition) the dierence between the nearest and arthest distance is itsel said to be the depth o. But we have to be very careul

5 Auto Accuracy Speciications Page 5 about that usage. Suppose that under deinition 1 the depth o or a sensor plane mm rom the lens ran rom mm to mm. (It always comes out symmetrical or deinition 1.) Then, the depth o, under that usage, would be stated as 0.08 mm. But o course i we are using the depth o as a tolerance limit on A error, does this mean that it is acceptable or the A system to produce the ly ed at a location that is o by 0.08 mm? o. It is only allowed to be o by 0.04 mm (one way or the other, o course) alling within the range o the depth o. To avoid any misunderstanding, its is better to say that the depth o in this situation is ±0.04 mm. And the A error tolerance speciication, under the within the depth o speciication, would best be said to be ±0.04 mm. THE SPECIICATIO We will assume here that when Canon states an A accuracy speciication as within the depth o, it is in light o our second deinition o its the only one that its the A accuracy model. However, or the cases o interest, the numerical limits or the two deinitions are essentially identical, so we really don t have to be concerned with which outlook they use. ote that here the DL is not one that we get to choose, but rather the one Canon has adopted as appropriate when stating A accuracy. I have heard that this is mm or ull-rame 35-mm sensor size cameras, and mm or cameras such as the EOS 20D. What determines depth o? Having chosen a DL criterion, the depth o depends on two parameters o the optical system: the actual diameter o the aperture o the lens (not the /number) and the distance rom the second principal point o the lens to the sensor. (The aperture o interest or our purpose is the maimum aperture o the lens, since that is the aperture in eect when the A process is conducted.) We normally reckon depth o or the situation in which the test object is at a distance much greater than the ocal length o the lens. Having done so, we can then replace the distance to the sensor with the ocal length o the lens. Then, having introduced the ocal length, we can rearrange the equation to use the /number rather than the actual diameter o the aperture. (And when we do that, the ocal length drops out altogether!) or the irst (normal) deinition, the depth o is given by: d = ±cn where d is the depth o (the single-sided value, thus the ± on the right side), c is the applicable DL, and n is the /number o the lens.

6 Auto Accuracy Speciications Page 6 or the second deinition o (the one that really pertains to this topic), the equation is much more complicated, but or any reasonable /number, the results are almost identical, so we won t bother with it here. I OBJECT SPACE So ar, our work has been totally in space, that is, in the region between the lens and the sensor. ow, on igure 3, we will direct our attention to object space, the region in ront o the lens. Our objective here is to relate the accuracy speciication in terms o to its impact on actual photographic work, and to eplore the relationship o that speciication to depth o ield. (a) Object (b) Object Plane o (diamater at DL) (c) y Object (d) y ar limit o depth o ield (e) "acceptable" y (diamater at DL) igure 3. Im seen in object space In Part (a) we see the situation in which the lens is ly ed on the object (at point ), meaning that a ly-ed o the object alls on the sensor. In Part (b), we see an A error such that the alls in ront o the sensor, and a blurred alls on the sensor. The degree o the error is such that the diameter o circle o conusion o the on the sensor is just the

7 Auto Accuracy Speciications Page 7 DL the on the sensor just barely meets the criterion o acceptable. This then corresponds to an A error that is just within the depth o In Part (c), we see that this corresponds to the system being actually ed at a point short o the object (point y). (This is the situation colloquially described by photographers as ront ing.) ow let s look at this rom another perspective. Part (d) o the igure shows the very same incorrect situation as shown in Part (b). ow, however, we have an object at point y, the point at which the lens is actually ed. That object will thus be given a ly ed on the sensor. In Part (e), we think o another object at point. We know rom Part (b) that an object at point would be d with blurring that was just acceptable under the applicable DL criterion. This is precisely the deinition o the ar limit o ield or on an object at point y. Hold that thought! ar limit o ield ear limit o ield (a) ocus at initial distance w y ar limit o ield ear limit o ield (b) ocus at nearer distance w (c) ar limit o ield ocus at arther distance ear limit o o ield ield igure 4. Symmetry o ield

8 Auto Accuracy Speciications Page 8 ow, to complete our story, let s look at igure 4, which shows an interesting symmetry in depth o ield. In Part (a), we see the camera ed on an object at point. The ar and near limits o ield or that situation are at points w and y. ow, in Part (b), we on an object at point y. It turns out that the ar limit o ield or that situation is precisely at point! Then in Part (c), we on an object at point w. It turns out that the near limit o depth o ield or that situation is precisely at point! This symmetry is not just an approimation, valid when the depth o ield is small compared to the distance; it applies or any situation (so long as none o the limits are at or beyond ininity). The mathematical proo is this is rather tedious, but you can readily demonstrate it empirically by playing with any competent depth o ield calculator. ow, with this in hand, returning to igure 3, Part (e), we now realize (rom igure 4) that i, or at point y, the ar limit o ield is at point (as shown in the igure), then or at point, the near limit depth o ield will be at point y. But, as seen in Part (c), point y is the nearest possible point o actual, under the within the depth o ield accuracy speciication, or attempted at point. Thus, we ind that the near limit o actual (but incorrect) distance or attempted on an object is precisely the near limit o ield or on that object. Precisely the corresponding relationship is true or the ar limits. This can be summarized: The range over which the actual distance can occur within the one depth o speciication o auto accuracy is eactly the same as the range o distance that constitutes the depth o ield or at the distance o our test object. Implications on photographic work This is o course a very useul act in assessing the practical photographic impact o potential A error. It means that a photographer, concerned over the possibility o A error, can: 1. Determine the in-speciication limits o ing error, in terms o distance, with any handy depth o ield calculator.

9 Auto Accuracy Speciications Page 9 2. Be comortable that, even with an A error o the greatest amount allowed under the speciication, the object ( target) will all within the depth o ield (even i the shot will be at the maimum aperture o the lens). THE 1/3 THE DEPTH O OCUS SPECIICATIO In many o the cameras o interest, Canon s A accuracy speciication or certain situations (or eample, or one o the center A detectors o certain cameras when the aperture o the lens is greater than a certain value) is within 1/3 the depth o. Does the happy situation we discussed above still apply here? That is, are the nearest and arthest distances at which the camera could, while still remaining within the 1/3 depth o tolerance, distances that are 1/3 as ar rom the object distance as the near and ar limits o ield? o, not quite. In act the ar limit o incorrect distance will not be quite as ar rom the object as 1/3 the distance rom the object to the ar limit o ield; the near limit o incorrect distance will be a little arther rom the object than 1/3 the distance rom the object to the near limit o ield. The precise distances that are the allowable limits o the distance under the within 1/3 the depth o speciication can, however, still be calculated using a normal depth o ield calculator. Just enter, as the value or the circle o conusion diameter limit (DL), a value that is 1/3 the actual DL Canon has adopted as the criterion o acceptable sharpness. The resulting near and ar limits o the depth o ield will be the allowable limits o distance under the within 1/3 the depth o speciication. ACKOWLEDGEMET Many thanks to Carla C. Kerr or her able and sensitive copy editing and prooreading o this manuscript. #