Methodology and Curve Interpretation

[Bill Burk]

Will this information allow me to take better photographs?

You already take better photographs.

 

[ic-racer]

The utility of a camera is to TAKE better photographs.
The utility of densitometry is to PRINT better photographs.

 

[aparat]

It's been a while since we discussed this, but I found this plot really interesting. It shows the log exposure axis in three different units. I probably wouldn't do it for every plot, but it is nice to have it and use it as reference. It's also a kind of textbook curve, showing distinct portions, marked a, b, c, and d, making it easy to identify them in case one wants to compute contrast, etc. It's kind of elegant in its simplicity, which I almost always like.

2023-02-27-0001 by Nick Mazur, on Flickr

 

[snusmumriken]

I am a scientist, so I do enjoy these technical aspects of photography. But I also relate to this quote from Elliott Erwitt, speaking of film choice, which I rediscovered today:
“I don’t like to make tests. I like other photographers to make tests and give me the results. I believe them.”

 

[aparat]

I made a plot that I want to share and ask your opinion. I was trying to come up with an "N versus EI" kind of plot based on the Way Beyond Monochrome method. The film's normal speed is determined in a separate test. Then, individual curve EI values are obtained for the Zone System N-number series (N-2, N-1, N, N+1, N+2). It's a very useful view of the data. Having said that, when I first read the chapter, I was confused as to where the data came from.

I think that this plot could be augmented by showing the actual N-numbers and EFS values for each curve in the family (green dots). This is possible because, in my test, film speeds are determined directly from the curve family. It's a slightly different approach. Is it useful to see both types of data points or am I complicating the issue?

Or maybe showing the data points is unnecessary? How about just plotting a curve that fits the data?

 

[ic-racer]

I’m very curious about this effective film speed. Is there any evidence to support it? Did Phil Davis just make it up?

 

[Stephen Benskin]

I vote for just plotting a curve that fits the data. It's cleaner. But we still have a question about correctly interpreting the data. Should we continue to perpetuate a misinterpretation of theory, or push toward a better understanding?

According to Safety Factors in Camera Exposure, "The fractional-gradient speed criterion (and its approximate equivalent, the simpler ΔX speed criterion described in Ref. 12) will continue to be useful as a supplement to the fixed-density speed criterion when an evaluation is desired of the effective picture-taking speeds of films that have been developed to average gradients higher or lower than the proposed standard average gradient. The fixed-density criterion tends to underrate films that are developed to a lower average gradient and to overrate films that are developed to a higher average gradient."

Almost any method will work to a satisfactory degree in the majority of cases because of the various controls, normal distribution, and lack of a need to be exact for a photograph to be successful. There's little need for those who use one film and one developer to have tight controls. Most conditions fall within a limited range and when the occasional extreme condition arises, if the photograph doesn't come out, it wasn't meant to be. But on a broader scale, over a larger population of materials, it begins to matter. The idea is for the method to be accurate and applicable with the greatest number of materials over most conditions. So while almost anything works under normal conditions with a short or medium toed film, how well will they work as the conditions become more extreme and with films with different toes?

A couple interesting observations. The first two from Theory of the Photographic Process, 3rd edition.

"The choice of grade is usually less critical than the choice of printing exposure." p 489

"Jones and Nelson studied the relation between the effective density ranges of negatives of 170 outdoor scenes and the log exposure ranges of the photographic papers that gave the best prints. The best print for each scene was chosen from a set of prints differing systematically in paper grade and in printing exposure. Several thousand prints were involved. According to the findings, a strong correlation exists between the density range of the negative and the log exposure range of the optimum paper only if the variations in the density range are due to differences in development, level of camera exposure, or type of film. When the negative density range varies because of differences in the luminance scale of the scenes, the correlation is weak. In fact, when the film characteristics, camera exposure, and negative development are accurately controlled and held at what might be called the “normal” level, there is a distinct tendency for observers to prefer prints made on the “normal” grade of paper (such as grade 2), regardless of the luminance scale of the scene. Although this tendency may seem odd, it appears to be confirmed by the common practice of photofinishing stations, where accurate control of the processing of films having uniform contrast characteristics has been found to allow the use of a constant grade of paper." p 489-490

Jones, L.A., and Nelson, C.N., Control of Photographic Printing: Improvement in Terminology and Further Analysis of Results, Journal of the Optical Society of America, V. 38, No. 11, 1948.

“Because of the influence of the brightness distribution and subject matter in the scenes photographed, an accurate prediction cannot always be made of the exposure scale (Log Exposure Range) of the paper which will give a first-choice print from a negative of known density scale (Density Range)… But what other course is there to follow? Either we must make the best of a somewhat imperfect relationship or face the prospect of having no criterion whatever for choosing the paper contrast grade.”

Within the simple line referring to the brightness distribution and subject matter in the scenes is the complex topic of subjective tone reproduction which makes all attempts at precisely quantifying the photographic process less than successful and allows for so many methodologies to work most of the time.

I find this graph telling. It shows the exposure range of the negatives that were all considered first choice prints on a grade 2 paper.

 

[ic-racer]

What a fantastic assortment of relevant quotes!!
These ideas could be posted over and over again to demonstrate the way things work.

 

[Bill Burk]

I’m very curious about this effective film speed. Is there any evidence to support it? Did Phil Davis just make it up?

Phil Davis just keyed 0.1 density above B+F to ASA speeds. Despite the fact that I strongly disparage following this moving speed point, I mark my own graphs with the moving 0.1 above base+fog points and label them with the corresponding EI.

It’s easy and illustrates how much that point moves with development changes.

But when I choose an exposure index of my own, I use Delta-X speeds for the planned development time.

That’s when I am shooting for excellent negatives. (like when I have a tripod).

As anyone else would do, I bend the speed a bit when shooting handheld in difficult lighting.

 

[Stephen Benskin]

Phil Davis just keyed 0.1 density above B+F to ASA speeds. Despite the fact that I strongly disparage following this moving speed point, I mark my own graphs with the moving 0.1 above base+fog points and label them with the corresponding EI.

It’s easy and illustrates how much that point moves with development changes.

But when I choose an exposure index of my own, I use Delta-X speeds for the planned development time.

That’s when I am shooting for excellent negatives. (like when I have a tripod).

As anyone else would do, I bend the speed a bit when shooting handheld in difficult lighting.

The key is you are making informed choices. As it should be.

 

[aparat]

I’m very curious about this effective film speed. Is there any evidence to support it? Did Phil Davis just make it up?

Yes, there is evidence to support the idea of an effective film speed, though the definition and approach vary somewhat depending on who you read. For example, Lambrecht and Woodhouse derive effective speeds by comparing one's sensitometric data against their development model (based on the Zone System, to some degree). Here's a plot that summarizes their approach. The EI values listed along the bottom of the graph are what the authors refer to as "effective film speeds." Phil Davis recommended using fractional gradient IDmin values as the basis for EFS calculations. Henry recommended a method that derived effective speed from a horizontal displacement of a characteristic curve, relative to a Zone V exposure (it's more complicated than that, but you get the picture), etc. There's no real consensus regarding effective speed in the literature, as far as I can tell. As @Bill Burk points out, it's probably a good idea to use a method that works in one's workflow, rather than hold on to a particular model too rigidly, especially if it's difficult to implement without specialist knowledge and instrumentation. And of course, there's always the safety factor to consider. Film can be supremely forgiving, especially these days, with so many people digitizing their negatives and adjusting contrast with Photoshop (or equivalent app).

 

[ic-racer]

Then, individual curve EI values are obtained for the Zone System N-number series (N-2, N-1, N, N+1, N+2).

My confusion stems from this sentence. What is the method to determine your EI used to create the graph of EI vs (anything).

 

[aparat]

As I was reading Way Beyond Monochrome again, I couldn't help but wonder about their proposed method of film testing involving photographing a step tablet on a light table with a macro lens or suitable bellows extension. It is a departure from a standard way of exposing film for sensitometric analysis by means of a sensitometer. One of the factors that varies across these two methods is the presence of flare. This made me think of the Jones and Condit (1941) paper.

It reminded me of the distinction that Jones and Condit make ( Loyd A. Jones and H. R. Condit, "The Brightness Scale of Exterior Scenes and the Computation of Correct Photographic Exposure*," J. Opt. Soc. Am. 31, 651-678 (1941)) between "negative material" (henceforth curve 1) and a "particular negative" (henceforth curve 2). They made it very clear that "If for any purpose it is desired to determine the magnitude of a negative density difference, delta Dn, corresponding to some object brightness difference, delta log Bo, curve 2 must be used. Thus, in dealing with tone reproduction problems which involve a consideration of gradients, curve 2 gives the desired information."

In that particular paper, the authors referred to the object as "Bo" or "brightness scale of the object" but, the term "object luminance" was also used, particularly, in later work. Curve 2 is derived by incorporating a flare factor, which is defined as the ratio of the brightness scale of the object to the illumination scale of the
image. In the classic tone reproduction theory, the more common representation of flare light is as a plot of log subject luminance to log image luminance, but in the paper above, we have both scene and image luminance plotted against negative density, i.e., a characteristic curve. This can be somewhat confusing, but I am just going to leave it at that, as, otherwise, I'd need to write a few paragraphs, and, besides, most of you already know this stuff really well.

What I do want to focus on is the fact that the proposed method for deriving curve 2 is rather involved. First of all, you need to know the actual brightness scale of the object, including the exact minimum and maximum values, which are related to the minimum and maximum negative densities related to that scene. You also need to, separately, expose a step tablet in a sensitometer, i.e., without flare, and plot it using the actual, rather than relative, exposure values. To derive curve 2, you also need to construct a separate log Bo scale (along the top of the plot in Fig. 4), and then measure displacement calculated from the brightness and flare information. It can be done, but it's rather tedious.

An alternative approach is to use the notion of flare light as "flare density," as suggested by Dorst ( Paul W. Dorst, "A Novel Graphical System for Representing Tone Reproduction Data," J. Opt. Soc. Am. 34, 597-600 (1944)) and others. The advantage of this approach is that you do not need to know the object brightness scale before the value of image density corresponding to any intermediate value of object density can be computed. In other words, it is possible to construct curve 2, without the complicated method proposed by Jones and Condit. You can even do it without knowing actual exposure values, by just using a relative LogE scale. That way, we can simulate a characteristic curve of the "particular negative" and compare it to the curve of the "negative material" rather simply. In my attempt to implement these two methods computationally, I obtained very similar results. They are not identical, and you can, of course, criticize the "flare density" model as not being "correct" but this might be a compromise that is worth making, particularly for the sake of simplicity. The chief distinction is that the "curve density" method is more of a simulation, whereas the "curve factor" method obtains actual measurements of parameters related to the negative in question. Since Jones and Condit tried to produce a large body of empirical data of actual scenes and actual negatives and prints, they, obviously, had to use the flare factor approach.

I synthesized a curve 1 (blue) to be similar to that in Fig. 4 above to make the comparison easier. I then used a flare ratio algorithm to derive curve 2 (red) and a flare density model to derive another curve 2 (green). Because the flare ratio method uses separation, the resulting curve 2 (red) becomes asymptotic past the point representing an object of zero brightness. The flare density curve 2, on the other hand, extends only as far as curve 1.

My point is not to argue that one model is better than the other. I am simply trying to find the simplest, but still reasonably accurate, method of deriving curve 2 for the purpose of analyzing gradients and simulating the mapping of negative density onto object brightness. I am curious to see what you guys think of these methods and how they compare. I am also curious to hear whether this type of analysis (i.e., curve 1 vs curve 2) is useful for ordinary film testing?

 

[aparat]

My confusion stems from this sentence. What is the method to determine your EI used to create the graph of EI vs (anything).

Yes, I was confused about this, too. They (Lambrecht and Woodhouse) explain it on p. 128, but the plot on p. 139 (Fig. 12) does not plot user data, which is why I made my plot, combining user and model data.

 

[Stephen Benskin]

My confusion stems from this sentence. What is the method to determine your EI used to create the graph of EI vs (anything).

ic-racer said:
I’m very curious about this effective film speed. Is there any evidence to support it? Did Phil Davis just make it up?


My interpretation of the question is a little different. Please let me know if I'm readying this wrong. The question is more of a statement and it strikes me less about how it's determined but the justification for the methodology used. What makes one methodology more or less correct? One of my concerns is these types of charts are typically lacking the basic assumptions that were used in determining the values. How is the user supposed to know the results will work for their conditions? What's the aim NDR that N is based on? I tend to also like to know if the assumed normal luminance range used is 2.10 or 2.20 logs. And let's not forget the flare value.

Side note: The term Effective Film Speed is used differently and in some cases used interchangeably with EI, but I like to think the basic distinction is that EI doesn't need to refer to a tested value while effective film speed should. In ANSI PH2.5-1979 Method for determining speed of photographic negative materials (monochrome, continuous-tone), section 7 Supplementary Speeds for Other Developers "In addition to the ASA speed, manufacturers and others may wish to determine a speed value for use in obtaining desired exposure levels when using developers giving development significantly different from the ASA developer. For determining these speed values, the exposure and evaluation method of tis American National Standard shall be used. These speed values shall not be stated as the ASA speed but shall be termed effective speeds."

 

[Bill Burk]

I’d carry a top hat out with me and set it on its side in a scene. Take a close-up meter reading from inside the hat and base the exposure on that reading, placing it at the lowest shadow value you can think of.

You ‘know’ the inside of the hat should have ‘no’ net density in the resulting negative except that because of actual flare there will be some density.

Plot that resulting density reading of the inside of the hat on the finished negative… on the curve from that film/development combination.

The displacement on the x-axis from where you placed it … to where it landed… defines the flare.

Convert the data points of the Log E scale of the graph to arithmetic numbers. Convert the difference (difference in Log E from where you placed the exposure to where density fell) to an arithmetic number and add this number to every exposure number and convert them back to Log.

Then find the density above each Log E result and plot that density above the original data point Log E position.

You’ll get the second curve from this exercise.

 

[ic-racer]

Again, without knowing how an EI is determined, I'm only guessing, but I suspect a disconnect between the empiric data from "panel of viewers" and "best print." Or I guess the question is "what is the connection?"

I do know that Delta-X connects 0.1log D to 0.3G via Delta-D and the parabola below. But what is the connection between this Exposure Index and 0.3G?

 

[ic-racer]

As I was reading Way Beyond Monochrome again, I couldn't help but wonder about their proposed method of film testing involving photographing a step tablet on a light table with a macro lens or suitable bellows extension. It is a departure from a standard way of exposing film for sensitometric analysis by means of a sensitometer. One of the factors that varies across these two methods is the presence of flare. This made me think of the Jones and Condit (1941) paper.

It reminded me of the distinction that Jones and Condit make ( Loyd A. Jones and H. R. Condit, "The Brightness Scale of Exterior Scenes and the Computation of Correct Photographic Exposure*," J. Opt. Soc. Am. 31, 651-678 (1941)) between "negative material" (henceforth curve 1) and a "particular negative" (henceforth curve 2). They made it very clear that "If for any purpose it is desired to determine the magnitude of a negative density difference, delta Dn, corresponding to some object brightness difference, delta log Bo, curve 2 must be used. Thus, in dealing with tone reproduction problems which involve a consideration of gradients, curve 2 gives the desired information."

View attachment 334357

In that particular paper, the authors referred to the object as "Bo" or "brightness scale of the object" but, the term "object luminance" was also used, particularly, in later work. Curve 2 is derived by incorporating a flare factor, which is defined as the ratio of the brightness scale of the object to the illumination scale of the
image. In the classic tone reproduction theory, the more common representation of flare light is as a plot of log subject luminance to log image luminance, but in the paper above, we have both scene and image luminance plotted against negative density, i.e., a characteristic curve. This can be somewhat confusing, but I am just going to leave it at that, as, otherwise, I'd need to write a few paragraphs, and, besides, most of you already know this stuff really well.

What I do want to focus on is the fact that the proposed method for deriving curve 2 is rather involved. First of all, you need to know the actual brightness scale of the object, including the exact minimum and maximum values, which are related to the minimum and maximum negative densities related to that scene. You also need to, separately, expose a step tablet in a sensitometer, i.e., without flare, and plot it using the actual, rather than relative, exposure values. To derive curve 2, you also need to construct a separate log Bo scale (along the top of the plot in Fig. 4), and then measure displacement calculated from the brightness and flare information. It can be done, but it's rather tedious.

An alternative approach is to use the notion of flare light as "flare density," as suggested by Dorst ( Paul W. Dorst, "A Novel Graphical System for Representing Tone Reproduction Data," J. Opt. Soc. Am. 34, 597-600 (1944)) and others. The advantage of this approach is that you do not need to know the object brightness scale before the value of image density corresponding to any intermediate value of object density can be computed. In other words, it is possible to construct curve 2, without the complicated method proposed by Jones and Condit. You can even do it without knowing actual exposure values, by just using a relative LogE scale. That way, we can simulate a characteristic curve of the "particular negative" and compare it to the curve of the "negative material" rather simply. In my attempt to implement these two methods computationally, I obtained very similar results. They are not identical, and you can, of course, criticize the "flare density" model as not being "correct" but this might be a compromise that is worth making, particularly for the sake of simplicity. The chief distinction is that the "curve density" method is more of a simulation, whereas the "curve factor" method obtains actual measurements of parameters related to the negative in question. Since Jones and Condit tried to produce a large body of empirical data of actual scenes and actual negatives and prints, they, obviously, had to use the flare factor approach.

I synthesized a curve 1 (blue) to be similar to that in Fig. 4 above to make the comparison easier. I then used a flare ratio algorithm to derive curve 2 (red) and a flare density model to derive another curve 2 (green). Because the flare ratio method uses separation, the resulting curve 2 (red) becomes asymptotic past the point representing an object of zero brightness. The flare density curve 2, on the other hand, extends only as far as curve 1.

My point is not to argue that one model is better than the other. I am simply trying to find the simplest, but still reasonably accurate, method of deriving curve 2 for the purpose of analyzing gradients and simulating the mapping of negative density onto object brightness. I am curious to see what you guys think of these methods and how they compare. I am also curious to hear whether this type of analysis (i.e., curve 1 vs curve 2) is useful for ordinary film testing?

View attachment 334364

Wow that it great, I always wondered where the flare curves that are so commonly thrown about come from.

 

[aparat]

Again, without knowing how an EI is determined, I'm only guessing, but I suspect a disconnect between the empiric data from "panel of viewers" and "best print." Or I guess the question is "what is the connection?"

I do know that Delta-X connects 0.1log D to 0.3G via Delta-D and the parabola below. But what is the connection between this Exposure Index and 0.3G?

Great questions! Here's my understanding of the concept. Maybe others will chime in to make it a more complete description.

The criteria for determining the speed of negative film (and other films) have changed over the years, some persisting today, others being forgotten by history. The idea of a fractional gradient, such as the 0.3Ḡ, was developed to offer a simple and reliable sensitometric criterion/measure of film speed, but, crucially, one that was in agreement with empirical studies of print quality.

Film speed, in theory, could be determined at any point along the curve by the function D=f(logE), but that is not very practical. Film speed could also be determined solely by psychometric (a.k.a., psychophysical) testing whereby a subjective determination of a high-quality print can be used as a criterion for film speed. However, neither a purely arbitrary sensitometric measure, nor a purely subjective one meets the criterion of being unique, reliable, and meaningful. Jones and Condit (and others) undertook studies to figure out the best way to measure film speed, given the above mentioned requirements and factors. To sum it up, they agreed that speed should be expressed in terms of a minimum exposure that yields a negative that results in an excellent print. I am trying to express decades worth of work in a single sentence, so forgive my leaving a lot of stuff out.

The sensitometric method that was found to be in a good compromise, or to be in good agreement, between sensitometric and psychophysical was the fractional gradient criterion. They found that the conditions of minimum exposure and excellent print quality were obtained at a point along the characteristic curve where the slope of the gradient is a "constant fractional part" of the average slope Ḡ of a portion of the curve extending the distance of ΔlogE = 1.5. When the gradient at the speed point is equal to 0.3Ḡ the exposure E0.3Ḡ determines the speed of that material, expressed as 1/E0.3Ḡ. Jones and Condit pointed out that, in their opinion, fixed density and fixed gradient film speed criteria were inferior because they "lacked significance as appraised by the yardsticks of excellent print quality and minimum camera exposure."

So, to conclude, one can choose from a number of different methods of determining their personal EI (or effective speed), including the fractional gradient method. It's a matter of personal choice. Film manufacturers, however, usually use the current ISO standard.

 

[Stephen Benskin]

So, to conclude, one can choose from a number of different methods of determining their personal EI (or effective speed), including the fractional gradient method. It's a matter of personal choice. Film manufacturers, however, usually use the current ISO standard.

The statistical psychophysical evaluation or print speed represents the most accurate method of determining film speed. Jones and Nelson compared the results obtained using various sensitometric methods to the print speeds as described in "A Study of Various Sensitometric Criteria of Negative Film Speeds." Obviously the psychophysical method would be "much too complicated and laborious to permit of its application in practice and that for such a purpose it is desirable or, in fact, imperative to find a sensitometric method which will yield results in close agreement with those obtained by the direct psychophysical method." It was concluded the fractional gradient method agreed most closely to the print speeds over the greatest number of films and situations. The Delta-X Criterion is the modern equivalent. It uses the same concept of the shadow gradient in determining the minimum useful exposure point and not density (a point that Jones greatly emphasized). The method has stood the test of time and why it is part of the current ISO standard.

One could say there is only one film speed and that is the speed at the fractional gradient point. Everything else is EI. In JOSA 1943, American Standard Method for Determining Photographic Speed and Speed Number, makes a distinction between "speed", meaning the fractional gradient speed, 1 / E, and "Speed Number", which is Speed / 4. Speed was "not intended for use with ordinary exposure meters or exposure calculators. The speed number was used as the published film speed. I believe they later became ASA Speed and ASA Film Exposure Index. While the published film speeds to be used in conjunction with an exposure meter aren't the actual speed determined at the fractional gradient speed point, they are tethered to the only method that has a legitimate connection to the subjective evaluation of quality. All other methods of film speed determination don't have that relationship and are compromised. My feeling is why go to the trouble of testing just to use an inferior method.

 

[ic-racer]

I'd consider "Speed" a scientific test of the film under controlled conditions.

I'd consider "Exposure Index" an occasionally uninformed free-for-all of "what ever works." For example the guy or gal that rates Tri-X at EI 1600 and brags about excellent shadow detail by placing the darkest shadow detail on Zone IV, etc.

 

[aparat]

The statistical psychophysical evaluation or print speed represents the most accurate method of determining film speed. Jones and Nelson compared the results obtained using various sensitometric methods to the print speeds as described in "A Study of Various Sensitometric Criteria of Negative Film Speeds." Obviously the psychophysical method would be "much too complicated and laborious to permit of its application in practice and that for such a purpose it is desirable or, in fact, imperative to find a sensitometric method which will yield results in close agreement with those obtained by the direct psychophysical method." It was concluded the fractional gradient method agreed most closely to the print speeds over the greatest number of films and situations. The Delta-X Criterion is the modern equivalent. It uses the same concept of the shadow gradient in determining the minimum useful exposure point and not density (a point that Jones greatly emphasized). The method has stood the test of time and why it is part of the current ISO standard.

One could say there is only one film speed and that is the speed at the fractional gradient point. Everything else is EI. In JOSA 1943, American Standard Method for Determining Photographic Speed and Speed Number, makes a distinction between "speed", meaning the fractional gradient speed, 1 / E, and "Speed Number", which is Speed / 4. Speed was "not intended for use with ordinary exposure meters or exposure calculators. The speed number was used as the published film speed. I believe they later became ASA Speed and ASA Film Exposure Index. While the published film speeds to be used in conjunction with an exposure meter aren't the actual speed determined at the fractional gradient speed point, they are tethered to the only method that has a legitimate connection to the subjective evaluation of quality. All other methods of film speed determination don't have that relationship and are compromised. My feeling is why go to the trouble of testing just to use an inferior method.

Thank you for putting this conversation in the context that I failed to communicate. I agree with you, in principle and in practice. If I was to, say, teach a workshop on this, I would choose a method that is most cogent from the point of view of theory and practice. I think that the original research by Jones and Condit was truly impressive and ahead of the curve. Scientists were just beginning to learn about human perception by means of quantitative methods. Harvey Fletcher's work in auditory perception comes to mind, but the field of visual perception was still in its infancy. What Jones did by combining quantitative and qualitative evidence was, in a sense, ground-breaking. What is more, he influenced the field for decades to come. I do not believe there was a study nearly as exhaustive in scope and substance since.

Having said that, I cannot help but also be impressed by photographers creating amazing art by using methods that, from the point of view of theory, seem haphazard, at best. People develop film in coffee and beer, digitize film with a DSLR, and still get great results. On the other hand, I test my materials as meticulously as I am able, and still end up with a roll of badly exposed frames from time to time. I just wasted two hours and three sheets of expensive paper trying to print from a badly exposed negative. I did get a decent print, but nowhere near good or even satisfactory.

 

[aparat]

I’d carry a top hat out with me and set it on its side in a scene. Take a close-up meter reading from inside the hat and base the exposure on that reading, placing it at the lowest shadow value you can think of.

You ‘know’ the inside of the hat should have ‘no’ net density in the resulting negative except that because of actual flare there will be some density.

Plot that resulting density reading of the inside of the hat on the finished negative… on the curve from that film/development combination.

The displacement on the x-axis from where you placed it … to where it landed… defines the flare.

Convert the data points of the Log E scale of the graph to arithmetic numbers. Convert the difference (difference in Log E from where you placed the exposure to where density fell) to an arithmetic number and add this number to every exposure number and convert them back to Log.

Then find the density above each Log E result and plot that density above the original data point Log E position.

You’ll get the second curve from this exercise.

This is a very ingenious method. Thank you for suggesting it. I have read about the black box with a hole, but not about the top hat. It should work even better than the box, especially if it's made of matte black felt, or similar fabric.

Right now, I want to do the Way Beyond Monochrome method from start to finish, including paper testing. Yes, I am aware of its shortcomings, but, in order to have a personal opinion, I need to apply the method in its entirety. I think of it as a learning experience.

I only have a medium format camera with extension tubes that give me 1:1 magnification, so I can use a 6x6 step tablet on a light table. The problem is, my densitometer's aperture is just barely small enough to measure a 21-step 6x6 target. I wish I had a way to verify my density measurements against a unit with a smaller aperture. Another option is using a larger step tablet and spreading the exposure over two or three 6x6 frames. I tried that a couple of times. It works but is cumbersome.

 

[Stephen Benskin]

Having said that, I cannot help but also be impressed by photographers creating amazing art by using methods that, from the point of view of theory, seem haphazard, at best. People develop film in coffee and beer, digitize film with a DSLR, and still get great results. On the other hand, I test my materials as meticulously as I am able, and still end up with a roll of badly exposed frames from time to time. I just wasted two hours and three sheets of expensive paper trying to print from a badly exposed negative. I did get a decent print, but nowhere near good or even satisfactory.

That's the art part and why there's no definitive quantitative method and why there is this forum and why we are still debating the issues. Speaking of which and something most of the general photography books tend to disregard is summed up in this quote by Loyd Jones, "Density, per se, has no significance as an indication of the ability of the photographic material to perform this function. the value of negative density..., for instance, the deepest shadow, is of no consequence except insofar as it may have some bearing on the exposure time required to make a print from the negative." This statement should bring into question the validity of any method that only uses density to determine exposure.

Jones is God. I once called Kodak, before they were a shell of a company, for information on Jones. Everyone I talked to responded the same. Oh, the guy who did the camouflage work. Funny that is what they remember him for.

There's a paper from a lecture by Jones that is a good overview of his lasting contribution. For those interested, Jones, L.A., The Psychophysical Evaluation of the Quality of Photographic Reproductions, PSA Journal, Vol. 17, Dec. 1951.

 

[aparat]

I blame @Stephen Benskin for making me go down the Jones rabbit hole again
I am kidding, of course. I enjoy reading this stuff, but it always fills my head with more questions than answers.

For example, Jones's stance on variable vs. fixed flare for the evaluation of optimal negative exposure in J. Opt. Soc. Am. 39, 94-135 (1949) is very interesting. He argues that the use of variable flare leads to two unwanted consequences: (1) the non-optimal value of Kn (a shadow detail compression factor), which ranges from too small to too large, relative to the optimal value of around 0.11, which had been derived from the earlier psychophysical studies. And (2), more importantly, a variable density range in the resulting negatives, necessitating the use of multiple paper grades. Instead, he argues, an average fixed flare factor of 4.0 is a better alternative because it results in a near-optimal value of Kn and does not change the resulting negative density range. He considers Kn to be the fundamental factor in the calculation of optimal exposure, with regard to obtaining excellent prints at the end of the chain, the value of 0.11 being the sweet spot, so to speak. The idea is summarized in these two tables:

Hope you guys can shed some light on this idea of fixed vs. variable flare.

Reading that paper also made me go back and add another function to calculate fractional gradient (0.3G) a little more accurately. The previous algorithm I used relied on finding the straight-line portion of the curve, so with some of the more highly distorted curves, it tended to underestimate the value. The one I just wrote, uses the method that Jones describes, except it doesn't require a pen and paper .

I am still trying to wrap my head around that crucial distinction he makes between negative material and a particular negative, especially in the context of tone reproduction, but I am not ready to formulate my questions yet.