What is the biggest, perfectly sharp format you can get from your sharpest negatives?

onnect17 said:

The book is titled "The photographic researches of Ferdinand Hurter & Vero C. Driffield"
You can find used copies in Amazon for $5 + shipping.
http://www.amazon.com/photographic-...=sr_1_1?s=books&ie=UTF8&qid=1297734069&sr=1-1

Click to expand...

Yes, I have the book. Where do I find the quote you mentioned?

A49 said:

As I can see we have the same DoF at different apertures in terms of F-stops .

In my point of view it makes no sense to mess up the use of f-stop values. You are right: The absolute diameter of the aperture opening of a 50 mm lens at f/4 and a 100 mm lens at f/8 is the same: 12,5 mm. But there are not many photographers that uses absolute diameters in practice.

The negative format does not play any role for the resolution kept on the film. It is only important for the maximum, still sharp print size that you can later obtain from the negative. So Ralph is right, when he says, that the DoF in terms of resolution is fixed in the negative. But Ralph is not right, if you look from the print format´s point of view. Then the DoF seems not to be locked in the negative and the DoF we observe in the print changes with the enlargement ratio for the print. There is no antagonism or paradox in it.

Best,
Andreas

Click to expand...

I underlined the important part, that's f-stop, it is not aperture, aperture is a linear measurement. Yes it makes NO sense to use different aperture values, HENCE you should test a 50mm at f/4 and a 100mm at f/8.

Otherwise it is akin to saying to having 2 rectangles with the same ratio, h1 and l1 = height and length, h2 and l2 = the same for rectange two. Then stating well h1 = l1/2 and h2 = l2/2 therefore l1 = l2.

f(1) / 4 is not equal to f(2) / 4, they are comlpetely different, because f(1) does not equal (f2). Therefore in such a test like Ralph's he is NOT isolating focal length, he is changing 2 things, and claiming one of them is causing DoF change, and not the other. If focal length controlled DoF and not aperture, the making the aperture smaller wouldn't increase DoF.



f/x is a method of easily relating exposure, in fact it is natural, and anyone who would work with diameter and focal length would straight away use the same formula for relating exposure, since with the diameter value you have to take into account focal length (or angle per unit of distance of gathering of light) to relate exposure from that.

Regardless of what you use, it doesn't chang facts, or physics.


Ralph's methodology of not isolating what he's claiming is the cause of effect is therefore flawed from the very beginning. It is the same as a person stating focal length affects perspective, and taking a picture of a subject on an 85mm lens, and then moving the camera forward to the subject and filling the frame at the same ratio (exactly the same as aperture ratio, this is how optics work) as the previous picture with a 24mm lens, then claiming "I changed the focal length from 100mm to 24mm and look at the difference in perspective!". This person didn't isolate the claimed cause of the effect, as we know the real cause is the change in distance to subject and ONLY distance to subject, focal length, yet again, has nothing to do with it.

RalphLambrecht said:

Andreas

There is nothing wrong with your numbers! Athiril's statement that all of your resolution values are above the diffraction values is not correct. If you take the near-IR threshold of 650 nm, the smaller f/stops are getting close to being borderline, but take the average of 555 nm, and your numbers are just fine. Also, your lens resolutions stated are well within the system performance of good equipment and materials.

Click to expand...

There is something SIGNIFICANTLY wrong with them, when f/22 has a diffraction limit 75% that of f/11 and so on.

smallest point = 1.22 (constant) * wavelength * f-number.
(http://en.wikipedia.org/wiki/Diffraction#Diffraction-limited_imaging)

I'm being generous and giving you 450 nm to work with instead.

So average finest lp/mm = (1000 / (1.22 * 0.45 *fn)) / 2

Therefore the following:

(on the negative).
f-stop --- resolution --- CoC
11 ------ 80 lpm ------- 0,013 mm
16 ------ 70 lpm ------- 0,014 mm
22 ------ 60 lpm ------- 0,017 mm
32 ------ 45 lpm ------- 0,022 mm
45 ------ 30 lpm ------- 0,033 mm
64 ------ 22 lpm ------- 0,045 mm
90 ------ 15 lpm ------- 0,067 mm
128 ----- 11 lpm ------- 0,091 mm
180 ------ 8 lpm ------- 0,13 mm
256 ------ 6 lpm ------- 0,17 mm


Becomes:



f-stop --- resolution ---
11 ------ 82.8 lpm -------
16 ------ 56.7 lpm -------
22 ------ 41.4 lpm -------
32 ------ 28.5 lpm -------
45 ------ 20.2 lpm -------
64 ------ 14 lpm -------
90 ------ 10.1 lpm -------
128 ----- 7.1 lpm -------
180 ------ 5.1 lpm -------
256 ------ 3.6 lpm -------

RalphLambrecht said:

Yes, I have the book. Where do I find the quote you mentioned?

Click to expand...

Page 301, second paragraph.

Athiril said:

There is something SIGNIFICANTLY wrong with them, when f/22 has a diffraction limit 75% that of f/11 and so on.

Click to expand...

As already wrote before the values for the F-stops f/11, f/16, f/22 are from real test (on film resolution), the rest are diffraction limits.

Athiril said:

smallest point = 1.22 (constant) * wavelength * f-number.
(http://en.wikipedia.org/wiki/Diffraction#Diffraction-limited_imaging)

I'm being generous and giving you 450 nm to work with instead.

So average finest lp/mm = (1000 / (1.22 * 0.45 *fn)) / 2

Click to expand...

Airy disk (smallest point) = 1.22 * wavelength * f-number

for instance the Airy disk for 546 nm and f-number 22

Airy disk = 1.22 * 546 nm * 22 = 0,0147 mm

the resolution for the above example resoltuion = 1/Airy disk = 1 / 0,0147 mm = 68 mm

There is no need to devide by 2, since the Airy disks may partly overlap and you see still two separated lines.

Best regards,
Andreas

Athiril said:

... I'm being generous and giving you 450 nm to work with instead.

So average finest lp/mm = (1000 / (1.22 * 0.45 *fn)) / 2
...

Click to expand...

Athiril

A49 is correct, you are not using the right equation.

Use resolution = 1/(1.22 * wavelength * N) to get max resolution. Using only mm and 555 nm for green light, it will return 5.8 lp/mm for f/256, which is, as I said, borderline to A49 proposed value.

I hope you can accept this 'pseudo scientist' proposal.

onnect17 said:

Page 301, second paragraph.

Click to expand...

Found it! Thanks.

Athiril said:

... Ralph's methodology of not isolating what he's claiming is the cause of effect is therefore flawed from the very beginning. It is the same as a person stating focal length affects perspective, and taking a picture of a subject on an 85mm lens, and then moving the camera forward to the subject and filling the frame at the same ratio (exactly the same as aperture ratio, this is how optics work) as the previous picture with a 24mm lens, then claiming "I changed the focal length from 100mm to 24mm and look at the difference in perspective!". This person didn't isolate the claimed cause of the effect, as we know the real cause is the change in distance to subject and ONLY distance to subject, focal length, yet again, has nothing to do with it. ...

Click to expand...

Athiril

Don't mix my claims with statements I have never made! Perspective can only be changed with viewpoint, not with a focal length change. I have never claimed anything else. Your two examples have nothing to do with each other. Mixing an uncomfortable but true claim from one person with a completely false claims of another is a common but shallow method to deceive. You shouldn't be doing that. This is either pretty low or you didn't really pay attention to what has been said.

Fact is, f/stop and focal length control DoF. You said, it's not true, only the opening of the lens (aperture) counts. Well, that true, but since focal length divided by f/stop equals the diameter of the aperture, you are saying the exact same thing. You are just using different terms. It makes no difference. The result is the same.

You said 100mm focal length at f/8 gives the same DoF as 50mm at f/4, because they have the same aperture. True again, but saying a 50mm lens will give more DoF than a 100mm lens at the same f/stop is also true, because they have different apertures. That was my pictorial example, by the way. You should agree with the conclusion made from it, because the two lenses used a different aperture per your correct definition, and you said aperture controls DoF. No need for a disagreement, but somehow you managed to modified the picture and proved to yourself that my conclusion was wrong, not realizing that your 'engineered' proof disagreed with your own statement as well.

You can't really support your disagreement with the aperture vs f/stop discussion. The term 'aperture' is commonly (mis)used to mean aperture value or f/stop. I agree, it is incorrect and inconsistent, but that's no reason to jump on the box and call people all wrong just to find out that they use focal length and f/stop instead of aperture but end up with the same values for DoF.

I must agree with one of the earlier posts. This has turned into a discussion about nothing. It doesn't help others, who read this thread, to have a petty argument about a common phrase and then use it to discredit perfectly correct statements about DoF. This only confuses people and I fail to see the point.

Anyway, with over 200 posts now, it's about time for me to do something else. I apologize if I got a bit aggravated with one or the other post. I get frustrated with the fact that written communication is just not as effective as a person-to-person conversations, but I should know better.

'Good Light' to everyone, and maybe Athiril and I can continue this conversation person-to-person at the photo outing in Melbourne on April, 2nd.

It is an analogy, people often claim focal length controls perspective (like I used to) because they often change subject distance with focal length, as that is typical usage, but not fact of the cause of effect.

Your claim was focal length controls DoF, but you are changing aperture along with it, if you do not change aperture, it doe notchange, therefore focal length is not having an impact on it, changing aperture (maintaining ratio) is typical usage, but it is not fact of the cause of effect. The cause of the effect is aperture.

lp/mm = line pairs per mm. lines/mm should equal the same thing, since the correct thing to do is to assume that it takes 2 lines to define, well 2 lines, 2 lines is going to equal 2 'points' in one direction. Therefore if the number of points per mm is equal to x, then lp/mm must equal to x/2, as 1 line pair = 2 adjacent points of detail.

Focal Length controls field of view alone.

"Fact is, f/stop and focal length control DoF. You said, it's not true, only the opening of the lens (aperture) counts. Well, that true, but since focal length divided by f/stop equals the diameter of the aperture, you are saying the exact same thing. You are just using different terms. It makes no difference. The result is the same."

Actually I said that focal length has no effect on DoF. F/stop already has focal length in it, you mean f-number and focal length. By which it doesn't, because focal length is removed from the equation by f/x, f/x tells you the aperture, when the aperture changes, DoF changes, when it doesn't DoF does not change (as in the zone of focus). I'm not saying the exact same thing, because you said focal length controls DoF, but your test has 2 different apertures as well as focal length.

Your central point of argument was that shorter lens on smaller format has a greater DoF advantage, with the central point of that being detailed.

I showed you can obtain both greater detail, and greater DoF for the same angle of view (greater focal length, balanced to the increase in format size).

This proves the following statement incorrect, and much the opposite: "DoF is much larger with the shorter lens (see the numbers above). Using such a lens, one has a better chance to get much more acceptable detail (definition of DoF) into the image."

Because you can obtain both greater detail (more lpph) and greater DoF at the same time with a bigger format and longer lens. The only test is detail and DoF, not aperture or f-stop, as the statement above says greater DoF with more detail, and that's all. The statement is not true.

It was a very informative thread in any case. Actually it is the kind of thread that only on APUG can take place. The level of technical knowledge inside here is quite elevated.

I like you all guys

Fabrizio

RalphLambrecht said:

Athiril

A49 is correct, you are not using the right equation.

Use resolution = 1/(1.22 * wavelength * N) to get max resolution. Using only mm and 555 nm for green light, it will return 5.8 lp/mm for f/256, which is, as I said, borderline to A49 proposed value.

I hope you can accept this 'pseudo scientist' proposal.

Click to expand...

You still need to multiply that by 1000 to get it up to mm, otherwise you are calculator single points per um, rather than line pairs for mm.

In any event that os the formula for the smallest point of detail.

1 lp = a pair of points.

Therefore 1 lp = 2 points. Therefore you still divide that by 2.


And even if you didn't. The values are still wrong, because his f/22 value is 75% of his f/11 value instead of 50%.

And if you didn't divide by 2, the f/11 value would be, most formula use 450 nm for a reason.

In fact, his f/11 value is using 450 nm as a value, its 80 lp/mm. If you didn't divide by 2 for lp/mm, his f/11 value should be 165.6 lp/mm, or 160 lp/mm in his rounded case, when you dont divide it by 2 (which is incorrect not to do)

For 555 nm f/11 would be 67 lp/mm, or if you incorrectly not divide by 2, it should be 134 lp/mm.

His values are way off. And the value should halve for every 2 f-stops given the above equation you gave, no matter how you use it with what wavelength.


IE: Given what you give above the chart would become the follow:

(converted from um to mm, and not accounting for the fact lp/mm is a pair of lines, and the above equation is for single points, not pairs, where you should divide by 2)

555 nm, 1 lp/mm counted as 1 point
f-stop --- resolution ---
11 ------ 134.25 lp/mm -------
16 ------ 92.3 lp/mm -------
22 ------ 67.13 lp/mm -------
32 ------ 46.15 lp/mm -------
45 ------ 32.82 lp/mm -------
64 ------ 14 lp/mm -------
90 ------ 23.08 lp/mm -------
128 ----- 11.54 lp/mm -------
180 ------ 8.2 lp/mm -------
256 ------ 5.8 lp/mm -------


Now you might think f/256 should be 5.8 lp/mm but this is the chart for the equation you give using 0.555 nm, you can see how wrong it is, and you should see where A49's chart is way off, it is completely inconsistent in values. f/11 = 80, but f/22 = 60? f/16 = 70, but f/32 = 45?


Compare it to the chart he gave:
f-stop --- resolution --- CoC
11 ------ 80 lpm ------- 0,013 mm
16 ------ 70 lpm ------- 0,014 mm
22 ------ 60 lpm ------- 0,017 mm
32 ------ 45 lpm ------- 0,022 mm
45 ------ 30 lpm ------- 0,033 mm
64 ------ 22 lpm ------- 0,045 mm
90 ------ 15 lpm ------- 0,067 mm
128 ----- 11 lpm ------- 0,091 mm
180 ------ 8 lpm ------- 0,13 mm
256 ------ 6 lpm ------- 0,17 mm



His values are not consistent with the equation for 555 nm and not dividing by 2.

In fact his f/11 value is 450nm and dividing by 2 (like it should be).

Athiril said:

It is an analogy, people often claim focal length controls perspective (like I used to) because they often change subject distance with focal length, as that is typical usage, but not fact of the cause of effect. ...

Click to expand...

Totally agree and always have.

Athiril said:

... Your claim was focal length controls DoF, but you are changing aperture along with it, if you do not change aperture, it doe notchange, therefore focal length is not having an impact on it, changing aperture (maintaining ratio) is typical usage, but it is not fact of the cause of effect. The cause of the effect is aperture. ...

Click to expand...

True, but how to phrase it depends on your point of view. Changing focal length and maintaining the same f/stop will change DoF. It's the same as you say, just using different parameters, and values I can set on my camera. I cannot select apertures in mm on my lenses.

Athiril said:

... lp/mm = line pairs per mm. lines/mm should equal the same thing, since the correct thing to do is to assume that it takes 2 lines to define, well 2 lines, 2 lines is going to equal 2 'points' in one direction. Therefore if the number of points per mm is equal to x, then lp/mm must equal to x/2, as 1 line pair = 2 adjacent points of detail. ...

Click to expand...

The diameter of the airy disc is 2.44. By using a value of 1.22 the division by 2 has already taken place. The equation used by A49 and I is correct (see attached). If you call that 'pseudo science' too, you're on your own.

Athiril said:

... Focal Length controls field of view alone. ...

Click to expand...

There is no reason to continue this discussion. It has turned into a ping-pong of arguments. There are no new points made. I posted an equation, which works for all common imaging conditions. Unless you can prove it wrong by showing a working alterative, which produces different but correct values, I'm not interested.

Show us your DoF equation! We know you have one, because you posted some values. What is it? Let's see it.

"The diameter of the airy disc is 2.44. By using a value of 1.22 the division by 2 has already taken place. The equation used by A49 and I is correct."

Look at my edited post, A49's values are inconsistent no matter how you use the equation.


"True, but how to phrase it depends on your point of view. Changing focal length and maintaining the same f/stop will change DoF"
Nobody argued that, I argued focal length has no effect. Just aperture. Changing the focal length and maintaining the same f/stop = changing the aperture.

But it has nothing to do with the following statement, which has been disproved:
""DoF is much larger with the shorter lens (see the numbers above). Using such a lens, one has a better chance to get much more acceptable detail (definition of DoF) into the image." "


Focal length has no influence on DoF, if you want to say otherwise you have to isolate and maintain a constant aperture, ie: like the perspective example, you cant move the camera forward or back to test perspective with focal length, you need to maintain the same absolute value to isolate it, not the same magnification of subject.

And it becomes diameter/4, so 1.22 doesn't account for that.

Athiril

You simply used the wrong equation. Use the one I posted, and you'll be fine.

Still like to see your equation for DoF, though. Waiting...

Athiril said:

"Look at my edited post, A49's values are inconsistent no matter how you use the equation.

Click to expand...

I get tired and exhausted to say the same things again and again, if you not read them thoroughly enough.

As I said the max. resolution values and related CoCs for f/11, f/16, f/22 are not from theory but from tests that proved what resolutions are possible with the very best LF lenses. There is absolutely no need and no use for calculating with a CoC 0,0076 mm for f/11 in LF (that equates 132 lpm diffraction limit for f/11 which is the half of diffraction limit at f/22 as you demanded). Nobody of us has ever seen a LF lens that at least comes close to the diffraction limit at f/11! (If there should exist any, then it is far too expensive for anything other than military or astronautic usage.)

For f/32, f/45, f/64, f/90, f/128, f/180, f/256 I used the diffraction limits (look in any book, you will find values that are nearly the same for shooting distances more than 10 times focal length of the taking lens). I used them because even average lenses will perform nearly at the diffraction limits if the aperture is closed to a f-stop beyond f/22.

This is the last thing that I say to my chart proposal. I think it delivers useful maxima for CoCs in LF. Think of it, use it or discard it.

May the spirit of the universe give us good light and high resolution for our next photographs!

Kind regards,
Andreas

A49 said:

(to Athiril)
I get tired and exhausted to say the same things again and again, if you not read them thoroughly enough. ...

Click to expand...

I know the feeling...

The equation 1.22 * wavelength * (focal length/aperture) gives you the diameter of the airy disc, not half the diameter. It is the smallest size of a possible single point, not a pair of points. A line pair is a pair of points. So as I stated, the many of values given by A49 are actually above the diffraction limit.


This is not the central issue however that you are straw-manning.

I like to look in the numbers regarding lens resolution not for other reason that I want to have an idea of "the amount of the loss", as a help selecting lens. If my lens perform the best at f/16, that's what I use, with wherever movements the view camera requires. If I think DOF is more important than resolution, then I would use a 3D camera.

Also keep in mind, unless your guys are contact printing, the scanning resolution needed to get all the information out of the negative have to be at least twice each value (Nyquist) and because we are talking about line pairs then the number is four.

Line Pairs
B-W B-W B-W

S_S_S_S_S_S Good 2X sampling
_S_S_S_S_S_ Bad 2X sampling (so 2X does not satisfy Nyquist)

SSSSSSSSSSS Good 4X sampling

Currently I'm scanning using around 160spi (4000dpi). I know the apo-sironar-s is giving me more than 40 lp/mm, but not much of the detail above that value is ending in my image file. This is one of the reasons I don’t use 8X10.

Athiril said:

The equation 1.22 * wavelength * (focal length/aperture) gives you the diameter of the airy disc, not half the diameter...

Click to expand...

Please indicate the source.

In all the literature I consulted the number is 1.22 and is associated with the first zero in the bessel funtion of the first kind, so is the radio of the cone.
Even in wikipedia is clear:

The factor 1.220 is derived from a calculation of the position of the first dark ring surrounding the central Airy disc of the diffraction pattern. The calculation involves a Bessel function—1.220 is approximately the first zero of the Bessel function of the first kind, of order one (i.e., J1), divided by π.

Source: http://en.wikipedia.org/wiki/Rayleigh_criterion#Explanation

There's some fundamental flaws with many of the equations when you reach the extremes of a lens performance particularly when stopped down at or near it's minimum apertures. So some lenses are still extremely sharp when in theory diffraction limitations should have made them near useless. Someone analysed John Sexton's published data (online a couple of years ago) for his images where lens & f-stop data's been published and what was interesting was that many of his images were made at f stops that many claim will suffer image degradation due to diffraction, yet there's no perceptible loss of image qualities.

In addition the DoF equations are simplified and so can't explain the differences in actual perceived DoF between images from two lenses of the same Focal length (designed for the same film format as well). The extreme of this is the DoF is greater at the same aperture for a Macro lens compared to a normal lens of the same focal length.

So in arguing over the theoretical a balanced overview is usually missing, that's why Craft is based on theory & Practice, and why people test for themselves as well, as Ralph's illustrated already.

Throwing another fly in the ointment the DoF and Diffraction equations take no account of the shape of the aperture/diaphragm and that has a profound effect on the appearance of out of focus areas, what many call the Bokeh. Then there's also the effects of a leaf shutter on DoF, so taking everything into consideration including lens design the reality is that only complex computer modelling can really make accurate mathematical predictions of sharpness and definition acr5oss the full gamut of apertures and particularly the smallest.

Ian

That's an excellent summing up Ian. My feeling is that the theoretical figures do not take into account the variables of lens design regarding defraction of the aperture and even lens coatings and I had lurking in the back of my mind something about leaf shutters creating a slightly different DoF, (possibly from one of L.P. Clerc's volumes). The absolute relevance of the figures seems to have little practical impact upon usage, or, at least, it shouldn't restrict it. However, Ralph's 'case' has been very illuminating, and consistent, and adds to my knowledge of how DoF is manifested, thankyou.
What was the original question ?

Mark Walker.

A problem with the standard DoF equations is that they only describe the initial step of a three-part process. They describe the formation of 'blur circles' in the focal plane of the lens, resulting from objects at various distances in front of the lens. (The equations are derived from geometrical optics using the thin-lens approximation and so can only be taken as a guide in any case). But in some ways the equations are meaningless as they stand, because the image only takes on a recognisable form after two further steps have occurred: (1) the image undergoes a linear magnification 'm', and (2) is then viewed from a distance 'd'.

It is interesting to consider the effect that these two additional variables have on the perceived DoF. If 'r' is the maximum resolution of the viewer's eye and 'd' and 'm' are defined as above, we can say that any blur circle on the original negative will be perceived by the viewer as indistinguishable from a point in the final print (and therefore may be considered to be sharp) provided that the diameter of the circle of confusion 'c' on the original negative is not larger than:

c = r x d / m

From this we can immediately see that if a standard viewing distance is adopted according to the size of the print from a given negative, the ratio 'd' / 'm' remains constant and it is appropriate to use a fixed value of 'c' in specifying the DoF marks on lenses. But we can also see that the viewer's perception of the DoF varies with the magnification and the distance of view.

How does this work with a practical example? (For the purposes of what follows, I ignore the maximum resolution of the lens/film/paper, each of which can add their own limitations). If I view an enlargement of a 35mm negative on 10x8 paper (say an enlargement of 7 times) from a distance of 10 inches and adopt a resolution of 1 arc minute for my eye, the value of 'c' becomes 0.011mm; for a viewing distance of 3 feet, 'c' becomes 0.038mm, and at 6 feet it is 0.076mm.

Suppose the photograph is of an object at a distance of 5000mm with a 50mm lens at f/4. We can use the equations from http://en.wikipedia.org/wiki/Depth_of_field to find the nearest and furthest distances of points from the lens that will result in circles of confusion of the sizes given above. The results are as follows:

'c' = 0.011mm, near DoF = 4559mm, far DoF = 5071mm, total DoF = 512mm
'c' = 0.038mm, near DoF = 3815mm, far DoF = 5388mm, total DoF = 1573mm
'c' = 0.076mm, near DoF = 3103mm, far DoF = 5909mm, total DoF = 2806mm

So by varying our distance from the print, we can significantly alter our perception of the DoF, possibly spoiling the photographer's original intentions. Of course, if the subject is isolated against a distant background, the increase in DoF may not be noticeable. We can also see from the above that the DoF expands rather than shrinking as we move away, so if DoF marks on lenses are set according to the minimum viewing distance, we will always get at least that much (thin-lens approximations notwithstanding).

Because I use a rangefinder camera and a TLR, I always use the DoF marks, but have never really given the subject much thought until now!

Athiril said:

The equation 1.22 * wavelength * (focal length/aperture) gives you the diameter of the airy disc, not half the diameter. It is the smallest size of a possible single point, not a pair of points. A line pair is a pair of points. So as I stated, the many of values given by A49 are actually above the diffraction limit.

This is not the central issue however that you are straw-manning.

Click to expand...

Athiril

Your equation is still wrong. You are confusing diameter with radius. You'll find the equation for diffraction-limited resolution in many books on optics and photography. Please look it up!

Your DoF equation is still missing, by the way.

Edward

Nicely followed through! How did you calculate the CoCs? I get 0.022 mm where you've got 0.011 mm.