Well thanks for the response anyway. My curiosity has been somewhat sated.
Fwiw I don't think that either is strictly "correct." Rather they are given as empirical methods where sometimes one seems to be a better predictor than the other.
My three opinions:
1. The modulation transfer functions of two parts of the system can be multiplied to get the MTF of the composite system. That's how MTFs are intended to work. If you do that, and define resolution as "the frequency at which the MTF is some value (like 20% or whatever)", then you will probably get a formula similar to: 1/f_total = 1/f1 + 1/f2, where the f's are frequency numbers such as 30 lp/mm. So if your two parts resolve at f1 = 50 lp/mm and f2 = 33 lp/mm, the composite resolution is f_tot ~= 20 lp/mm.
2. If you define resolution as spot size, then you can convolve (not multiply) the spot diameters of two parts of the system to approximate the spot diameter of the total. Convolution means that the diameters are added in quadrature. This is described by: d_tot^2 = d1^2 + d2^2. So for example if the spot sizes produced by the two parts of the system were d1=0.02mm (1/50 mm) and d2=0.03mm (1/30 mm), the composite spot diameter is d_tot ~= 0.036 mm (1/27 mm).
If you figure that the spot size is about the reciprocal of the resolution frequency, d ~ 1/f, you can see that these two formulas work out fairly similar, though not exactly the same. It is my guess that the formula cited by Erwin Puts was a garbled version of argument #2.
3. My third opinion is that you don't need to know any of this stuff for pictorial use. I am a research scientist and do optical and angular resolution calculations for work, so I have to think about it at work. But for pictorial use, it would be better to practice nailing your focus, stopping down to f/5.6-8 as needed, and using a tripod where possible. I don't stay up late worrying about the resolving power of film.
My three opinions:
1. The modulation transfer functions of two parts of the system can be multiplied to get the MTF of the composite system. That's how MTFs are intended to work. If you do that, and define resolution as "the frequency at which the MTF is some value (like 20% or whatever)", then you will probably get a formula similar to: 1/f_total = 1/f1 + 1/f2, where the f's are frequency numbers such as 30 lp/mm. So if your two parts resolve at f1 = 50 lp/mm and f2 = 33 lp/mm, the composite resolution is f_tot ~= 20 lp/mm.
2. If you define resolution as spot size, then you can convolve (not multiply) the spot diameters of two parts of the system to approximate the spot diameter of the total. Convolution means that the diameters are added in quadrature. This is described by: d_tot^2 = d1^2 + d2^2. So for example if the spot sizes produced by the two parts of the system were d1=0.02mm (1/50 mm) and d2=0.03mm (1/30 mm), the composite spot diameter is d_tot ~= 0.036 mm (1/27 mm).
If you figure that the spot size is about the reciprocal of the resolution frequency, d ~ 1/f, you can see that these two formulas work out fairly similar, though not exactly the same. It is my guess that the formula cited by Erwin Puts was a garbled version of argument #2.
3. My third opinion is that you don't need to know any of this stuff for pictorial use. I am a research scientist and do optical and angular resolution calculations for work, so I have to think about it at work. But for pictorial use, it would be better to practice nailing your focus, stopping down to f/5.6-8 as needed, and using a tripod where possible. I don't stay up late worrying about the resolving power of film.
I'd GUESS that a lot of higher end lenses for 35mm cameras would also do so in the center. But they gotta be faster than f/2. If they don't do it, as is, narrowing down the wavelength range with a sharp blue or green gel filter would probably do it.
My three opinions
If it were a high-contrast litho film this would probably be judged as higher resolution simply because the difference shows up more.
"Empirical" means the opposite of that, maybe the word you're looking for is "heuristic"?Well thanks for the response anyway. My curiosity has been somewhat sated.
Fwiw I don't think that either is strictly "correct." Rather they are given as empirical methods where sometimes one seems to be a better predictor than the other.
One thing about the resolution chart is its "vagueness" in a certain range. There's no specific judgement for contrast, just do you see a probable separation of steps or not? So the contrast of the film probably plays a role also. If it were a high-contrast litho film this would probably be judged as higher resolution simply because the difference shows up more.
If we had 3 people rate a "standard" resolution target we'd likely have 2 or 3 different ratings. Similar, but different.
Yes. But its important to note that people often misunderstand the nature and function of resolution as its more a property of quality (refinement) than it is of quantity.
For instance, many will think that a sharper picture has a higher level of resolve, but this usually isn't the case.
So remember that resolution is effected primarily by contrast, not acuity.
There was a review on YouTube on the Leica Summicron 50mm APO f/2 vs the Zeiss Planar 50mm f/2. The reviewer disliked the Zeiss since it showed more contrast…!
There was a review on YouTube on the Leica Summicron 50mm APO f/2 vs the Zeiss Planar 50mm f/2. The reviewer disliked the Zeiss since it showed more contrast…!
Zeiss T coated lenses are known to be resolution champs.
The reviewer admitted the Zeiss was in the same league as the Leica APO, and surpassed it in some respects…!
How did the reviewer determine the resolution of the two lenses? Eyeballing it perhaps?
"Empirical" means the opposite of that, maybe the word you're looking for is "heuristic"?
More to the point - look up which Zeiss Tokina 35mm lenses have actually been adapted to microchip printing applications. It's not like those are expected to perform as well as dedicated fixed focal length, fixed aperture lenses made for that specific purpose, but it does provide a clue.
Meanwhile, "apo" means all kinds of things. In the case of ordinary lenses, it means something distinctly less stringent than it does in the graphics trade. I have a set of true Apo Nikkor graphics lenses, and they exceed anything marketed as "apo" under general photography auspices. Very expensive Apo EL Nikkor lenses (not to be confused with mere EL Nikkor enlarging lenses) have been used for sophisticated LF scanning backs related to forensic sleuthing and copying fine paintings. Now those have been replaced by dedicated systems, but it furnishes yet another clue to the difference between industrial and consumer optics. You can get pretty much anything you want for a price, including custom machining.
I'm only stating this to imply how the expression, "apo", can get stretched like a rubber band to fit all kinds of thing. Sometimes it's just a marketing tweak implying, "better, improved".
More to the point - look up which Zeiss Tokina 35mm lenses have actually been adapted to microchip printing applications. It's not like those are expected to perform as well as dedicated fixed focal length, fixed aperture lenses made for that specific purpose, but it does provide a clue.
Meanwhile, "apo" means all kinds of things. In the case of ordinary lenses, it means something distinctly less stringent than it does in the graphics trade. I have a set of true Apo Nikkor graphics lenses, and they exceed anything marketed as "apo" under general photography auspices. Very expensive Apo EL Nikkor lenses (not to be confused with mere EL Nikkor enlarging lenses) have been used for sophisticated LF scanning backs related to forensic sleuthing and copying fine paintings. Now those have been replaced by dedicated systems, but it furnishes yet another clue to the difference between industrial and consumer optics. You can get pretty much anything you want for a price, including custom machining.
I'm only stating this to imply how the expression, "apo", can get stretched like a rubber band to fit all kinds of thing. Sometimes it's just a marketing tweak implying, "better, improved".
Tokina has ample quality control muscle. The items they make for Zeiss labeling seem to be excellent. But what they make for a lower price point, potentially under their own label, might be something different.
Let me provide a similar case from my own background. I set up the first Makita showroom in this country, back when every power tool they offered was true industrial quality. That was decades ago. Today they still make not only true industrial tools, but even have an aerospace division including items made for NASA. But they're very big company making various grades of tools for sake of different markets. So when you walk into a Home Depot, the version of Makita they sell is mostly made in China and at the low end of the totem pole when it comes to quality. The good stuff is mostly made in Japan, the US, and Germany instead. They have their own plants in all these countries.
What is Bosch-labeled is analogous, and can vary all the way from OK quality consumer tools (mostly made in Malyasia), to very high quality equipment made in the US and Germany. You get what you pay for.
Tokina isn't that huge of a company, but is still a well-equipped subcontractor capable of making a variety of quality grades, and even potentially setting up factories in more than one country based on labor rates etc. So I certainly wouldn't worry about them making lenses for Zeiss, even if you're had less than ideal experiences with some of their other items.
More to the point - look up which Zeiss Tokina 35mm lenses have actually been adapted to microchip printing applications. It's not like those are expected to perform as well as dedicated fixed focal length, fixed aperture lenses made for that specific purpose, but it does provide a clue.
Meanwhile, "apo" means all kinds of things. In the case of ordinary lenses, it means something distinctly less stringent than it does in the graphics trade. I have a set of true Apo Nikkor graphics lenses, and they exceed anything marketed as "apo" under general photography auspices. Very expensive Apo EL Nikkor lenses (not to be confused with mere EL Nikkor enlarging lenses) have been used for sophisticated LF scanning backs related to forensic sleuthing and copying fine paintings. Now those have been replaced by dedicated systems, but it furnishes yet another clue to the difference between industrial and consumer optics. You can get pretty much anything you want for a price, including custom machining.
I'm only stating this to imply how the expression, "apo", can get stretched like a rubber band to fit all kinds of thing. Sometimes it's just a marketing tweak implying, "better, improved".
What does a story about Makita and Bosch tools at Home Depot have to do with Tokina making Zeiss lenses? And I thought it was Cosina/Voightlander than made the manual focus lenses for Zeiss in different mounts.
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