Doug Kerr
Well-known member
In this note, I will talk about two related matters in the context of the Canon EOS autofocus system, the best focus correction value (BFCV) and AF micro-adjust (MA).
Phase Comparison
The Canon EOS AF system revolves around the quantitative determination of the "error" in the current focus setting through what is often called phase comparison.
Its principle is essentially the same as what is done visually in a split image focusing aid.
For each AF point, there are two little image detectors, which I will call "AF subdetectors". They both regard the same small zone of the scene, but they have their own aperture stops, much smaller than the actual aperture stop of the lens. These are located off center, on opposite sides of the lens axis.
If the current focus setting for the scene material in the field of view of these subdetectors is perfect (that is, would result in the image being formed precisely on the actual sensor during the shot), then (in a simple model of the system) the images cast on the subdetectors will exactly align (just like the two adjacent visual images on a split-image focusing aid).
If focus is not perfect, the images will not align. The amount of misalignment is a quantitative indicator of the amount by which the image would be formed in front of or "behind" the sensor (measured along the lens axis). The relationship depends on the separation of the two little "subapertures" and other geometric quantities, and is known for any body design.
But, unlike the two image areas in the visual focusing aid, the two subdetectors are not actually located adjacent on the chip that carries them. They are displaced (just to make room - there are actually a lot of them, sometimes eight for an AF point!)
But for each subdetector, a "relay lens" in the path is aimed so as to to make the two images fall on corresponding places in the two subdetectors in the case of perfect focus. But maybe not exactly (the mechanical arrangements might not be perfect).
Accordingly, a number that tells how the locations of images on the two subdetectors, observed with respect to an arbitrary reference point on each subdetector, would relate for the case of perfect focus, determined by testing after the camera is assembled, is stored in non-volatile memory in the camera.
Then, in actual operation, the locations of the two images on their subdetectors, expressed with respect to the reference point on each, are compared, and then this adjustment value is subtracted. The resulting number is taken as the focus error (again, in terms of the distance of the planned where the image would fall from the plane of the sensor).
The autofocus process proceeds based on that value, both in reckoning the amount of lens focus mechanism movement that should bring focus to "perfect", and in confirming at the end of the whole cycle that focus is indeed now "perfect" (within an established tolerance).
Spherical aberration
If a lens has truly spherical surfaces (and traditional lens design has been predicated on that - for one thing, it is "relatively easy" to accurately create such a surface) we do not get the behavior we would like, which is that for a point on the object all the rays entering the lens will converge at a single point in the image.
Rather, all the rays passing through the aperture at a certain distance from its center will converge in a point, but all the rays passing through the aperture at a different distance from the center will converge at a place that is either closer to the lens or farther from it that the first rays.
This phenomenon is described as spherical aberration. It means that there is no place we can put the sensor such that a point on the object will result in a point on the image - a "blur-less" rendering.
There is a place at which the cross-section of the set of all rays, heading toward their respective points of convergence, is the smallest in diameter, and we might think that if we arrange for that to fall at the sensor, we will get the sharpest image possible under the conditions.
But our perception of the diameter of the blur figure is not based on its overall diameter. The rays are more concentrated toward the center, and we judge its size based on that.
It turns out that for a location where the overall diameter is a bit larger than the smallest available, the distribution of the rays is such that the perceived diameter is the smallest. Placing the sensor there will thus result in the sharpest perceived image.
That situation is in fact called the "best focus" situation.
Now the degree of spherical aberration can be mitigated in various ways - using lens surfaces that are not spherical, combining lens elements with different indexes or refraction, and so forth. Doing this is a major preoccupation of lens designers.
But we never can eliminate the phenomenon completely in a context where we will be using the lens to focus the camera at different distances and will use different apertures for different shots. So a compromise design is used.
The remarks above about blur figure size and "best focus" apply to lenses in which spherical aberration has been mitigated (but not eliminated).
Back to phase comparison
The AF subdetectors each work with rays through a small subaperture, essentially all rays passing through the overall aperture at a small range of distances from its center. Accordingly, these rays will very nearly converge at a point (even though there is in fact spherical aberration in the lens).
But "ideal focus" on the subdetectors (where the rays all converge at the same point) does not necessarily correspond with "ideal focus" on the sensor, which gives the best perceived sharpness when all the rays do not focus at the same point.
The best focus correction value (BFCV)
In order to deal with this, just before any phase comparison measurement is made (such as at the beginning of an AF operation), the lens delivers to the body a value called the best focus correction value (BFCV). That says, in effect:
The body then takes the focus error as indicated by phase comparison, adjusts it by the recently-received BFCV, and uses that as the focus error for further work.
The ultimate result of this tampering with the indicated focus error is that the focus state to which the AF system seeks to place the lens will differ from where it would seek to place it, based on the actual measured focus error, by that adjustment amount.
(It is just like lowering the temperature to which a thermostat takes the room by heating the thermostat's detector a little, thus tampering with its perception of temperature error.)
Where does the lens get the BFCV it delivers?
The BFCV typically depends on, for any particular lens (model and copy):
• The zoom setting (if a zoom lens)
• The current setting of the focusing mechanism
In fact, in many case, for any combination of those, the lens delivers two BFCV's, one applicable to the spacing of the subapertures in a "standard" AF detector, and one to the (greater) spacing of the subapertures of a "long baseline" AF detector (the ones that require an aperture of f/2.8 or better).
In older Canon EF lenses (the only ones on which I have many details of this, and that only from considerable reading between the lines of the service manuals), the blue delivered is worked up this way:
• There is a "table" of the values, presumably depending on the two parameters mentioned above, that is part of the firmware for the lens model, stored in ROM.
• There is a set of adjustments to the standard table values, to precisely particularize them for this individual copy, burnt into a different area of the ROM at the factor after testing when the lens copy has been assembled.
• There is a further set of adjustments to the standard table values (as already adjusted by the per-copy adjustments in ROM) that can be changed in the field. They are carried by electrical jumper settings (pairs of PC board pads that can be shorted together with solder drops). Often there is a single such adjustment value applicable to all the standard AF detector values and another one applicable to all the "long baseline" AF detector values.
(Yes, you have to take the lens partly apart to get at these. In some cases, this only requires removal of the "tail cone".)
The units of the BFCV
The nature of the BFCV is as an adjustment to the measured longitudinal focus error in image space. It is a distance, and can be thought of as being in mm.
I do not know the actual encoding used to deliver the BFCV or its precision or unit. However, it is fairly certain that the basic unit is the single-sided depth of focus for the maximum aperture of the lens, based on the holy Canon value of circle of confusion diameter limit (CoCDL), 0.035 mm. It turns out that this unit is, in mm:
0.035N (mm)
where N is the f-number.
The increment of the "solder-drop" adjustment is usually 1/2 or 2/5 of the single sided depth of focus.
Enter AF micro-adjustment
Modern Canon EOS bodies have a feature called AF micro adjustment (MA).
This allows a user to store in the camera focus error correction values for individual lenses (that is, the user's copies).
I believe that separate corrections can be stored for different combinations of focus setting and (where applicable) zoom setting.
My belief is that this is just a further layer of the BFCV story. That is, at least for the older EF lenses I mention above, the actual BFCV used by the AF system is the concatenation of:
• The table value from the standard table for that lens model (for the zoom setting, if applicable, and focus setting in effect).
• The adjustment for the particular lens copy stored in the second area in ROM.
• The field adjustment stored in the solder-drop jumpers (there is always a value, although it might be the default, which is handily "no solder drops").
• The applicable MA value stored in the body for this lens (and perhaps this zoom and focus distance situation).
The unit
It has been reported by one of our colleagues here that the unit of MA setting (I understand that one an set values over the range of ±20 units) is 1/8 the single-sided depth of focus.
For an f/2 lens, that would be a distance of 0.00875 mm.
Significance in object space
Keep in mind that this value applies to a shift in focus error in image space (shift in the position of the image with respect to the sensor plane).
We of course become aware of focus error in object space; that is, the departure of the plane of best object focus from the plane containing our "target" ("front- or back-focus").
That is related to the focus error in image space by a straightforward (if not trivial) mathematical relationship, which I will not discuss here. The relationship depends on the focal length of the lens and the distance to the target.
To put it into perspective, assume a focus error of 1/8 the single-sided depth of focus (the magnitude of one unit of MA adjustment) in the direction that leads to back focus.
Assume a 50 mm f/2.0 lens and a target at 3000 mm (118.1 inches, almost 10 feet).
Then the amount of back focus resulting from that image space focus error would be about 36 mm (about 1.4 inches).
Norms
Again by way of perspective, Canon's published norms for overall AF accuracy of an EOS camera are ±1 single-sided depth of focus for "standard" AF detectors, and ±1/3 the single-sided depth of focus for "long baseline" AF detectors.
In the service manuals for some of the early EF lenses, the target for accuracy of the lens itself (presumably in a "perfectly calibrated" test body) is ±1/4 the single-sided depth of focus. Although this is not explicit, this might be for both detector types.
Acknowledgment
My thanks to my colleague Wilba from the ProPhoto Home forum, who pointed out to me recently the role spherical aberration plays in this story.
Best regards,
Doug
Phase Comparison
The Canon EOS AF system revolves around the quantitative determination of the "error" in the current focus setting through what is often called phase comparison.
Its principle is essentially the same as what is done visually in a split image focusing aid.
For each AF point, there are two little image detectors, which I will call "AF subdetectors". They both regard the same small zone of the scene, but they have their own aperture stops, much smaller than the actual aperture stop of the lens. These are located off center, on opposite sides of the lens axis.
If the current focus setting for the scene material in the field of view of these subdetectors is perfect (that is, would result in the image being formed precisely on the actual sensor during the shot), then (in a simple model of the system) the images cast on the subdetectors will exactly align (just like the two adjacent visual images on a split-image focusing aid).
If focus is not perfect, the images will not align. The amount of misalignment is a quantitative indicator of the amount by which the image would be formed in front of or "behind" the sensor (measured along the lens axis). The relationship depends on the separation of the two little "subapertures" and other geometric quantities, and is known for any body design.
But, unlike the two image areas in the visual focusing aid, the two subdetectors are not actually located adjacent on the chip that carries them. They are displaced (just to make room - there are actually a lot of them, sometimes eight for an AF point!)
But for each subdetector, a "relay lens" in the path is aimed so as to to make the two images fall on corresponding places in the two subdetectors in the case of perfect focus. But maybe not exactly (the mechanical arrangements might not be perfect).
Accordingly, a number that tells how the locations of images on the two subdetectors, observed with respect to an arbitrary reference point on each subdetector, would relate for the case of perfect focus, determined by testing after the camera is assembled, is stored in non-volatile memory in the camera.
Then, in actual operation, the locations of the two images on their subdetectors, expressed with respect to the reference point on each, are compared, and then this adjustment value is subtracted. The resulting number is taken as the focus error (again, in terms of the distance of the planned where the image would fall from the plane of the sensor).
The autofocus process proceeds based on that value, both in reckoning the amount of lens focus mechanism movement that should bring focus to "perfect", and in confirming at the end of the whole cycle that focus is indeed now "perfect" (within an established tolerance).
Spherical aberration
If a lens has truly spherical surfaces (and traditional lens design has been predicated on that - for one thing, it is "relatively easy" to accurately create such a surface) we do not get the behavior we would like, which is that for a point on the object all the rays entering the lens will converge at a single point in the image.
Rather, all the rays passing through the aperture at a certain distance from its center will converge in a point, but all the rays passing through the aperture at a different distance from the center will converge at a place that is either closer to the lens or farther from it that the first rays.
This phenomenon is described as spherical aberration. It means that there is no place we can put the sensor such that a point on the object will result in a point on the image - a "blur-less" rendering.
There is a place at which the cross-section of the set of all rays, heading toward their respective points of convergence, is the smallest in diameter, and we might think that if we arrange for that to fall at the sensor, we will get the sharpest image possible under the conditions.
But our perception of the diameter of the blur figure is not based on its overall diameter. The rays are more concentrated toward the center, and we judge its size based on that.
It turns out that for a location where the overall diameter is a bit larger than the smallest available, the distribution of the rays is such that the perceived diameter is the smallest. Placing the sensor there will thus result in the sharpest perceived image.
That situation is in fact called the "best focus" situation.
Now the degree of spherical aberration can be mitigated in various ways - using lens surfaces that are not spherical, combining lens elements with different indexes or refraction, and so forth. Doing this is a major preoccupation of lens designers.
But we never can eliminate the phenomenon completely in a context where we will be using the lens to focus the camera at different distances and will use different apertures for different shots. So a compromise design is used.
The remarks above about blur figure size and "best focus" apply to lenses in which spherical aberration has been mitigated (but not eliminated).
Back to phase comparison
The AF subdetectors each work with rays through a small subaperture, essentially all rays passing through the overall aperture at a small range of distances from its center. Accordingly, these rays will very nearly converge at a point (even though there is in fact spherical aberration in the lens).
But "ideal focus" on the subdetectors (where the rays all converge at the same point) does not necessarily correspond with "ideal focus" on the sensor, which gives the best perceived sharpness when all the rays do not focus at the same point.
The best focus correction value (BFCV)
In order to deal with this, just before any phase comparison measurement is made (such as at the beginning of an AF operation), the lens delivers to the body a value called the best focus correction value (BFCV). That says, in effect:
For this lens, at its current focus mechanism position, for some assumed shooting aperture, and for the standard locations of the phase comparison subapertures in EOS bodies, the focus should be shifted from perfect focus, as indicated by the phase comparison system, by this much [the BFCV] to produce best focus.
The body then takes the focus error as indicated by phase comparison, adjusts it by the recently-received BFCV, and uses that as the focus error for further work.
The ultimate result of this tampering with the indicated focus error is that the focus state to which the AF system seeks to place the lens will differ from where it would seek to place it, based on the actual measured focus error, by that adjustment amount.
(It is just like lowering the temperature to which a thermostat takes the room by heating the thermostat's detector a little, thus tampering with its perception of temperature error.)
Where does the lens get the BFCV it delivers?
The BFCV typically depends on, for any particular lens (model and copy):
• The zoom setting (if a zoom lens)
• The current setting of the focusing mechanism
In fact, in many case, for any combination of those, the lens delivers two BFCV's, one applicable to the spacing of the subapertures in a "standard" AF detector, and one to the (greater) spacing of the subapertures of a "long baseline" AF detector (the ones that require an aperture of f/2.8 or better).
In older Canon EF lenses (the only ones on which I have many details of this, and that only from considerable reading between the lines of the service manuals), the blue delivered is worked up this way:
• There is a "table" of the values, presumably depending on the two parameters mentioned above, that is part of the firmware for the lens model, stored in ROM.
• There is a set of adjustments to the standard table values, to precisely particularize them for this individual copy, burnt into a different area of the ROM at the factor after testing when the lens copy has been assembled.
I do not know whether this is in true ROM - write once only - or if it can be rewritten in the field.
• There is a further set of adjustments to the standard table values (as already adjusted by the per-copy adjustments in ROM) that can be changed in the field. They are carried by electrical jumper settings (pairs of PC board pads that can be shorted together with solder drops). Often there is a single such adjustment value applicable to all the standard AF detector values and another one applicable to all the "long baseline" AF detector values.
(Yes, you have to take the lens partly apart to get at these. In some cases, this only requires removal of the "tail cone".)
The units of the BFCV
The nature of the BFCV is as an adjustment to the measured longitudinal focus error in image space. It is a distance, and can be thought of as being in mm.
I do not know the actual encoding used to deliver the BFCV or its precision or unit. However, it is fairly certain that the basic unit is the single-sided depth of focus for the maximum aperture of the lens, based on the holy Canon value of circle of confusion diameter limit (CoCDL), 0.035 mm. It turns out that this unit is, in mm:
0.035N (mm)
where N is the f-number.
The increment of the "solder-drop" adjustment is usually 1/2 or 2/5 of the single sided depth of focus.
Enter AF micro-adjustment
Modern Canon EOS bodies have a feature called AF micro adjustment (MA).
This allows a user to store in the camera focus error correction values for individual lenses (that is, the user's copies).
I believe that separate corrections can be stored for different combinations of focus setting and (where applicable) zoom setting.
My belief is that this is just a further layer of the BFCV story. That is, at least for the older EF lenses I mention above, the actual BFCV used by the AF system is the concatenation of:
• The table value from the standard table for that lens model (for the zoom setting, if applicable, and focus setting in effect).
• The adjustment for the particular lens copy stored in the second area in ROM.
• The field adjustment stored in the solder-drop jumpers (there is always a value, although it might be the default, which is handily "no solder drops").
• The applicable MA value stored in the body for this lens (and perhaps this zoom and focus distance situation).
The unit
It has been reported by one of our colleagues here that the unit of MA setting (I understand that one an set values over the range of ±20 units) is 1/8 the single-sided depth of focus.
For an f/2 lens, that would be a distance of 0.00875 mm.
Significance in object space
Keep in mind that this value applies to a shift in focus error in image space (shift in the position of the image with respect to the sensor plane).
We of course become aware of focus error in object space; that is, the departure of the plane of best object focus from the plane containing our "target" ("front- or back-focus").
That is related to the focus error in image space by a straightforward (if not trivial) mathematical relationship, which I will not discuss here. The relationship depends on the focal length of the lens and the distance to the target.
To put it into perspective, assume a focus error of 1/8 the single-sided depth of focus (the magnitude of one unit of MA adjustment) in the direction that leads to back focus.
Assume a 50 mm f/2.0 lens and a target at 3000 mm (118.1 inches, almost 10 feet).
Then the amount of back focus resulting from that image space focus error would be about 36 mm (about 1.4 inches).
Norms
Again by way of perspective, Canon's published norms for overall AF accuracy of an EOS camera are ±1 single-sided depth of focus for "standard" AF detectors, and ±1/3 the single-sided depth of focus for "long baseline" AF detectors.
In the service manuals for some of the early EF lenses, the target for accuracy of the lens itself (presumably in a "perfectly calibrated" test body) is ±1/4 the single-sided depth of focus. Although this is not explicit, this might be for both detector types.
Acknowledgment
My thanks to my colleague Wilba from the ProPhoto Home forum, who pointed out to me recently the role spherical aberration plays in this story.
Best regards,
Doug
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