What is the total resolution of a combined system?

[raghavsol]

Hi,
According to common sense, if I have an optics of let say 120 lp/mm resolution then I must select a sensor of at least 120 lp/mm resolution to get over all resolution of the combined sytem (optics+sensor) equal to 120 lp/mm. But this is not correct because total resolution (Rt) is given by following relation:

1/Rt^2 = 1/Ro^2 + 1/Rs^2, where Rt is total resolution of optics+sensor system, Ro is optics resoluiotn and Rs is that of sensor.

I am not able to comprehend this can anybody help me?

In other words I can put my doubt this way; what kind of resolution is required for the sensor to record all the information provieded from the lens?

Raghav

[Struan Gray]

1/Rt^2 = 1/Ro^2 + 1/Rs^2

This is only true if the blur from your optics and the blur from your sensor have a particular functional form - usually assumed to be Gaussian: the famous bell curve.

Lenses have blurs which at best are Airy functions. These are much steeper than Gaussians for a given normalisation.

Film has blur which is very process-dependent, and which is complicated by the mixing of spatial and tonal resolution once you get down amongst the grain.

Empirical research has shown that 1/Rt = 1/Ro + 1/Rs is a better expression for photographic imagery. It fits with the general observations above.

For a digital sensor the blur is again based upon Airy functions, so I would expect the combination of reciprocals to hold there too. I am sure the NSA have worked out all the details.

[Walter Calahan]

This only matter if the images produced on a system of any resolution are worth looking at. Some of the best images ever made were on sensors (film) that could not come close to the resolving power of the lens.

[Emmanuel BIGLER]

If I dare to add my 0,02 euro here.
Before trying to combine resolution figures, it might be useful to define the resolution figure itself...

Traditional resolution figures for lenses were, in the past, defined by the minimum feature size visible on a high-resolution film recording the image of a resolution target. The image has to be carefullly examined with a good microscope.
This classical procedure is still in use by serious authors on the web like Christopher Perez.
However the resolution figure of 120 cycles/mm is hardly ever useful in the real photographic world except when you enlarge microfilms in order to extract a precious document recorded optically.

A more satisfactory approach would be to know the modulation transfer function of the lens and define the resolution by the maximum cycles/mm capable of rendering a minimum acceptable contrast in the final image.
If you insist on, say, 40% of minimum contrast, I know no photographic optics covering medium or large format capable of such a performance, except, may be, some specialised process lenses of the old times like the Zeiss Orthoplanar.

When a lens is listed @120 cycles/mm like some top-class MF lenses on Chris Perez's web site, it means the those 120 cy/mm are still visible, but vanishing, at something like 5% of contrast. So the same lens at 40% contrast will only resolve.. I do not know, but 60 cy/mm would already be outstanding.

Regarding the empirical law quoted by Struan about adding the inverse resolution figures and not the squares, it can be related to some real mathematical process of multiplying two FTM curves for two subsequent imaging processes.
If you make a simple model for the low frequencies and represent the FTM curve as a straight line starting at 100% for zero cycles end gently falling down to 0% of contrast at some absolute resolution limit, if you multiply two curves of the same kind you get a "curved" curve which slope at the origin obeys exactly Struan's "empirical" law.
In other terms, Struan's law 1/Rt = 1/Ro + 1/Rs has the following meaning : the slope for the combined MTF curve, extrapolated from its beginning around zero cy/mm as a straight line until crossing the zero-contrast line,yields a combined resolution of 1/Rt = 1/Ro + 1/Rs

Now what happens with digital ? Things become really tricky.
I have played the game of comparing the MTF curve of a modern fine-grain colour slide film (Fuji Provia 100) and the expected MTF curve of an ideal digital sensor with a pixel pitch of 7 microns and 100% coverage with side-to-side square pixels.
There is a first difficulty with the Bayer sensor, since the pixels of the same R, G, or B colour are located with a pitch of 14 microns, not 7, but imagine that the pixels are true RGB pixels on an ideal grid with 7 microns pitch.
With this simple model, taking into account some anti-aliasing filter to limit the resolution at 70 cycles/mm, the actual limit according to the sampling theorem, you find that the 7-micron pitch digital sensor has roughly the same FTM curve than provia 100F slide film.

If you do not use any anti-alising filter, the actual resolution limit given by the modeled FTM curve of the sensor would be something like 140 cy/mm but you cannot re-construct without aliasing any fine cycles beyond the limit of 70 cy/mm.

But in the real world, what you get out of your digital sensor might not be a really raw digital data, manufacturers do not give so much information about what they actually do inside the sensor before delivering the image, and they are free to manipulate the image ad libitum, they can boost the MTF curve up to the sampling limit by any proprietary algorithm ... and taking into accound that European, laws, to date, do not recognise software patents, do not expect to see the alogorithms described anywhere on any public document !!

As a conclusion, this is another story that may explain, eventually, after this long discussion, why I am dubious about defining the resolution by a single figure related to the minimum feature size at the limit of detection of vanishing visibility is not really meaningful.

I prefer to look at the contrast achieved for 10, 20 and 40 cycles/mm like in manufacturer's specs. For a 10x enlargement observed at a distance of about 300mm (12") , considering taht the eye has a resolution limit or 5 to 7 cy/mm in thios conditions, the important number of cy/mm on film or sensor are betwen 50 and 70, not 120.
And between 50 and 70 cy/mm, whereas the good old film cannot but let its FTM curve drop down to zero, digital sensors helped with unlimited booting algorithms can keep an excellent contrast up to the limit imposed by the sampling theorem.

Yes, I admit that this is cheating, definitely unfair with respect to the old & respectable film technology...

The ftm curve for provia 100F film can be found here
http://www.fujifilm.com/products/pro...Provia100F.pdf
The curve, when re-plotted in a linear horizontal and vertical scales, is very close to the simple sin(x)/x FTM model for a digital sensor fitting with anti-aliasing filter cutting at 70 cy/mm. Boosting the FTM of the sensor means artificially keeping the mtf contrast as close to 100% as possible until the final cutoff of the filter. No anti-aliasing filter would mean : set the resolution limit to about twice the value at 140 cy/mm with a 7 micron pixel pitch, this will in principel deliver about 60% of contrast at 70 cy/mm without any pre-processing of the image ; with the hope that your subject has no fine grids beyond 70 cy/mm generating aliasing or moiré artefacts. Or that you can post-process those artefacts by some other smart-cheating procedure

Suggested readings on Norman Koren's site
http://www.normankoren.com/Tutorials/MTF1A.html

[Emmanuel BIGLER]

Sorry, the link to the Provia datasheet liste above is broken, I have found another one that works :
http://www.fujifilm.fr/support/pdf/f...Provia100F.pdf

In this official document, the MTF curve (see page 6) stops at about 60 cy/mm at 35% of contrast, and up to this published value, both curves for this film and a 7 micron pitch ideal sensor with anti-aliasing filter are very similar.
Above 60 cy/mm there is no data availble for provia film, but since it has been tested well above 100 cy/mm by independant measurement (Zeiss people among others), it means that the MTF curve does not drop as abruptly as the sensor's with anti-aliasing filter.
Unfortnately as far as I know, it seems very difficult to measure MTF curves above 100 cy/mm, so the only accessible values come from the traditional method of the vanishing visibility of a recorded test target.
Unfortunately for film, the tail of the film MTF curve, although it certainly continues up to 150 cy/mm with a few % of contrast (which I truly believe), does not make the print sharper visually since in the competition for visual sharpness, the digital sensor boosted by all enhancement procedures can keep a high contrast up to 60 cy/mm.

To me the consequence is that defining the resolution for optics + film by the limit of perception at a low contrast does not properly reflect the quality of images that one can actually print and examine, say, at a 10X enlargement ratio.

[Ken Lee]

When a lens is listed @120 cycles/mm like some top-class MF lenses on Chris Perez's web site, it means the those 120 cy/mm are still visible, but vanishing, at something like 5% of contrast. So the same lens at 40% contrast will only resolve.. I do not know, but 60 cy/mm would already be outstanding.

I can grasp the first point, quoted above: much of the high resolution data, when using film with superb lenses, is lost - because it is low in contrast. It is "vanishing visibility".

I can also grasp the idea that a digital sensor can recover some of that "vanishing" data.

What I don't follow, is your conclusion. What does this tell us about film, versus digital sensors ?

[Steven Barall]

You people know too much.

[Nathan Potter]

What I think Emmanual is saying is that if you specify a very high image frequency (>100 lp/mm.) your image on film is going to be of very low contrast and visually appear to be of poor resolution due to the discrimination capability of the human eye. OTOH if one puts a pixelated sensor at the film plane, instead of film, and choose a spacial frequency of modest dimensions (say 50 lp/mm.) the functional form of the image collection is no longer a classic Airy function but a square wave function where each pixel picks off a discrete part of a COC (Circle Of Confusion). I imagine that constructing a mathematical connection between the Airy function and the square wave function would be quite complicated. (Maybe a square wave function is not the proper form here - I'm no expert)

But in practice I suspect that the higher contrast possible with a digital sensor at modest spacial frequencies is part of the reason why the digitally captured image can be so astoundingly good at times. (Not to mention the signal processing enhancements possible within camera)

Nate Potter

[Bruce Watson]

You people know too much.

Is that possible?

[Emmanuel BIGLER]

What I don't follow, is your conclusion. What does this tell us about film, versus digital sensors ?
Ken, my conclusions are exactly the same as Nathan's.

For the same surface, provia film and a sensor with 7 micron pitch plus anti-aliasing filter have the same resolution, in fact their MTF curve is similar.
Film can go much beyond 70 cy/mm, I have found the reference to tests at Zeiss : Resolving power of photographic films, Zeiss
Camera Lens News N° 19, mars 2003
available from the Zeiss web site http://www.zeiss.de

But the digital sensor can be boosted by all kinds of secret tricks inside the electronics, close to the sensor. So the contrast of the digital image can be boosted up to stay as high as possible up to the absolute limit of 70 cy/mm in the example cited above. And I know that some correcting software can manage moiré effects in prost-processing, in other words the anti-aliasing filter might not be necessary at all.
And the noise is much lower in a silicon detector, this is not a digital effect, it is due to the quantum efficiency of silicon compared to film. This efficiency commands the noise factor for a given amout of photons received per pixel.
Best films have a quantum efficiency of about 1%. Good old tri-X is rated at something like 0.5 % ; whereas curent amateur-grade silicon photo sensors reach 10 to 20% ; professional sensors for astrophysics and space programs exceed 80%.

Although I know all the advantages, I do not really care for them my amateur photography, I stay with film in MF and LF.
I know on a scientific basis that I need big film-pixels to get a good image with invisible noise; in LF, film resolution becomes a non-issue with respect to lens resolution in modern lenses.
In conclusion : I do not care : I use a big camera and I enjoy to see real images on a real support !
I like to do the traditional darkroom and I do not want to manage a family photo archive digitally.
I have inherited of all may father's B&W negatives since 1935.
I have all his kodacrhomes (35mm) slides from 1960.
I do not do anything special to manage this archive, the images are stored in boxes at home. At no cost and I can, any time, retrieve an image visually and print it. Yes often the images are scratched, but the image are there.
I have no clients, no production stresses and short delays, most advantages of digital image capture & processing are minimal for me. I need a good print : no problem, now that digital prints from film are top-class, I know how I can do if I do not want to print them myself in the darkroom.