Simulating color reversal films - DIR couplers

[AbsurdePhoton]

Hi there, I had posted things only in the B&W section, now it is the turn of color films.

For those who don't know, I am trying to simulate analog films in a software which is for the moment not publicly published, but i will surely do that when I consider the simulation good enough.
The good news is I am also simulating the printing process now (only paper for the moment). All works pretty well for B&W, I obtain good negatives and I can simulate regular and multi-grade B&W papers.

But I had a hard time understanding how color negative films work, you can count several weeks, and it is not finished. I have attained a satisfactory simulation for color negatives : I combine the spectral sensitivity curves, H&D curves, dye curves, for the films themselves and the printing part uses color compensating filters in a virtual enlarger (Kodak Wratten filters).

But --- something is still wrong. I obtain what seems to be good negatives (overall orange hue), they look convincing. But when I virtually "print" them, the colors are good but a LOT faded, no matter how I play with the virtual color compensating filters (which in fact mostly modify the color balance, nothing else).

I think I found what I missed, an essential part : the DIR couplers.

What I understand is that when a dye is formed, at a certain level there is something that also forms, the DIR couplers, that prevent in a certain extent the other dyes to form. And this is chemical. So this is a system of "dominant" dye that "boosts" the colors. My result is good, but it misses saturation. If I boost the saturation in Gimp, the photo looks well printed.

Could someone here explain the process in details, so that I could imagine a way to simulate the DIR couplers ?
Another question : are there also DIR couplers in printing papers ?

Thanks in advance.


( here is an example with Kodak Gold 200 + Kodak Ektacolor Edge 7 : original, negative, print without color filters - I used a pretty much saturated source photo for the demo )

source image : https://wallpapers.com/wallpapers/english-longhorn-beef-cattle-breed-h6zojezohim1ld7e.html

 

[koraks]

The dominant factor seems to be a contrast/gamma mismatch, and that doesn't look like a DIR coupler problem.

If I boost the saturation in Gimp, the photo looks well printed.

?

I see a gamma problem, not a saturation problem?

Another question : are there also DIR couplers in printing papers ?

I don't think so, no. The simple reason is that they're not necessary since the problem of crosstalk between the color layers is avoided in other, simpler ways that are not possible in a recording material.

Your question should be answerable on the basis of publications in the IS&T domain. Some of that may be accessible, although much/most of it is behind institutional paywalls. Have you done a literature search yet?

 

[Rudeofus]

DIR couplers do not directly inhibit dye formation, they inhibit photographic development. Unlike restrainers they don't do this all the time, but only after reacting with an oxidized color developer. This whole thing happens in three steps:

Ag+ + CD-4 <===> Ag + CD-4OX
CD-4OX + DIR <===> CD-4-phenol + powerful restrainer
Ag+ + powerful restrainer <===> undevelopable Ag+

As silver gets developed, more and more restrainer is released and development in this region slows down. Dependent of how color layers are arranged on your film, this development inhibitor can diffuse into adjacent layers, e.g. as more green/magenta is developed, blue/yellow and red/cyan are also more restrained, giving you more saturated colors. This is how film makers create "vivid colors" versus "natural colors".

 

[Lachlan Young]

Couplers etc aren't the problem here, it's understanding how the mask gets automatically (and properly) corrected out in a darkroom situation. If you think about how the mask works, what the paper is effectively 'seeing' would equate to the areas of greatest mask density (i.e. negative rebate) being the white point pre-inversion.

The DIR/ DIAR couplers affect not just the colour correction, but aspects like sharpness (and achieving 100%+ contrast response at very low frequencies is something digital really cannot do), apparent 'granularity' from the dye clouds and highlight density control.

 

[koraks]

it's understanding how the mask gets automatically (and properly) corrected out in a darkroom situation.

I wonder how the mask was modeled here in the first place. It's kind of abstract to me since the mask in reality will have a significant role in terms of the spectra of the primary dyes and the (density-dependent!) correction that the mask applies over this, but since we're in digital space here, there's also the interaction with the (hypothetical, simulated?) scanner which has a certain spectral sensitivity. So I wonder if I'm looking at the simulated color negative, what it really is I'm looking at.

Taking it for a spin for a manual inversion exercise, the only thing I can tell for sure is that the image does not respond like any scanned color negative I've ever seen. I don't know what's wrong with it exactly, only that it's not representative for how a scanned color negative looks like in reality. The clipping in the blue channel doesn't help either, but that's not the main problem. There's something about the curve shape that's very odd.

This is what a real color negative does if you take a scan of the negative and apply a simple linear curve to it:

As you can see, it doesn't go totally wonky-bananas. You also typically end up with a rather flat positive this way, which makes sense due to the curve shape of a typical RA4 paper, which is both steep and has a pronounced toe & shoulder. If you apply a toe + shoulder to the digital curves, things start to look more like what you'd expect a print to come out like:

 

[AbsurdePhoton]

Thanks for these answers !

@koraks : if I boost the saturation OF THE PRINT the result looks better, not the developed state. The developed state is just a visualization, the real values are kept as Transmittance of the film, to be fed to the printing part.

Somewhere in my workflow, for each discretized wavelength value, I do :
densityTotal = densityYellow + densityMagenta + densityCyan + densityMin (the last one is what gives the developed film its orange hue, is this the "mask" you're all talking about ?

densityTotal multiplied by an output spectrum (for each discretized wavelength value) is what gives the "negative" image, it is just for visualization, for example with daylight spectrum, after converting the discretized spectrum to the XYZ color space then converted back to RGB. I think that should give a good hint at what a negative looks like. So there's a a gamma problem at this step.

@koraks again : could you post the negative scan of the village scene ? I'd like to see what you mean by "the image does not respond like any scanned color negative I've ever seen", so I can test it myself.

About the different curves : I am keeping all the original values, without distorsion. The only thing i do to the HD curve is transforming it to relative exposure (just a translation to 0). But I have the exposure and time compensation values to get back to the "real" output density values (i.e. I don't use "real, physical" exposure and time compensation values)

About the inhibiting couplers : I think I will have to include that for at least the saturated colors effect. I can use the MTF curve to simulate the sharpening (and inversely blurring) effect.

Thanks again to all of you.

 

[koraks]

could you post the negative scan of the village scene ?

Sure, no problem; here you go:

Keep in mind that this is on Kodak Vision3 50D, so the color balance is way different than what you'd typically see on C41 film.
This was scanned as a positive/slide, judging by the frame edges I used a FlexTight Precision II for this. All adjustments were disabled in the FlexColor scanning software. So this is pretty much WYSIWYG. Note how flat this is compared to the digitally simulated negative you posted in #1.

Here's another one, this time on Kodak Ektar, so perhaps more representative. But it's also scanned on a different scanner (Minolta Scan Dual IV); same principle though - scan as slide/positive, with no adjustments.

This negative is somewhat overexposed and in terms of color balance there's the issue of rather strong UV in the hills in the background as I used no UV filter on this shot. While the color balance looks rather different, this is in part due to scanning software settings and a certain degree of auto-balancing that happened in the background.

What you would ideally obtain is a digitization of a color negative that is made with some kind of photospectrometer or at least a calibrated color densitometer, so you have a more solid baseline. Scans are always kind of iffy in terms of the black-box behavior of a scanner and the accompanying software. For most of us amateur snapshotters that's not really a problem, but for the kind of thing that you're doing, it's a big issue as it introduces a set of moving targets that's difficult to grapple with.

I mentioned the IS&T publications earlier; there's a good reason I did this. Much of what you're running into was dealt with in great depth around 20-30 years ago esp. by Kodak and its affiliates. They faced the challenge of having to digitize motion picture film and then reconstruct the image with faithfulness in relation to the optical printing materials that were being used at the time - and also in parallel to some of the digitization efforts. This led to a great deal of research into characterizing the color negatives and various interaction effects within the film itself and between the negatives and processing devices. If you can find a way to access the IS&T publications of that era, I'm sure there's lots to learn there that can save you a great deal of experimenting, second-guessing and getting lost on goose chases.

 

[AbsurdePhoton]

I searched a little and I could get a scan of the SPSE Handbook of Photographic Science and Engineering, 1973. Is this the same book as the IS&T you are talking about, but an earlier version ? In this one chapter 7 is about photography, 7.7 about dyes. I'll read that !

 

[koraks]

I'm not referring to a particular book.
IS&T is the Society for Imaging Science and Technology: https://www.imaging.org/
There's a library link that allows to search their publications here: https://library.imaging.org/ However, full text of those articles is for the most part not publicly accessible AFAIK. Maybe you can access through an institution you have an account with, or try some kind of backdoor.

 

[Lachlan Young]

the SPSE Handbook of Photographic Science and Engineering

It contains the baseline knowledge needed to deal with making photographic materials - i.e. the fundamental engineering principles involved in things like colour neg film & print papers, how the dyes and masks operate etc (and the relevant matrix maths). It also outlines analytical techniques for material characterisations and analysis. The relevant information is spread across 4 chapters or so. There is data that shows how masking via coloured couplers works.

Going further than that will require you to get stuck into Hunt et al.

However it does not touch significantly on things like DIR/ DIAR as those were highly commercially sensitive at that point in time - and are, I'd suggest, perhaps somewhat irrelevant to what you are attempting to do at this stage. More to the point, how do you intend to achieve an MTF response that is (e.g.) 120% at 20 cyc/mm?

 

[laser]

I cannot adequately explain the entire reproduction system data collection that is needed in this limited space. However, I suggest you consider a less ambitious modeling color negative film based on using a spectral exposing source to expose film and reading the spectral densities of the resulting dye images produced at several densities. This should include the camera produced color negative image and the printing system. This “print through analysis” will identify the impact of the film. It is not a trivial task. The result will identify what influence each of the major imaging components (i.e. film or paper) has on the resulting image. It will not tell you the impact of each of the technologies i.e. masking, colored couplers, DIR, inter-image effect, spectral sensitivity, various scavengers, silver image creation, dye image creation, curve shape, flare etc.

In building films, hundred if not thousands, of film coatings are made to determine the effect of the components then those results are used in statistically designed experiments analyzed by regressions. They are then combined and analyzed many more times. This will indicated the actions and interactions that will determine the imaging results. I believe attempting to separate the results without individual and mixed component testing is impossible. There are too many variables.

I am reluctant to post this because I am not prepared to thoroughly describe all the work that is necessary to complete the modeling. I hope the information gives you some guidance.

 

[AbsurdePhoton]

Thanks for all the tips, you all ! And thanks to @koraks for the negatives. I didn't plan this, but feeding a scan of a negative instead of a source image seems to be a good idea : analyzing and feeding it to the printing part will require only a few modifications. And it will also work for B&W negatives.

@Lachlan Young : applying a MTF curve is done in the frequency domain. I convert the image to the frequency domain, construct an adequate frequency domain representation of the MTF curve, combine the two, get back to spatial domain - magically, the sharpening and blurring effects appear ! All of course is done taking in account the source image resolution, which was the part I was missing at the beginning, and made me sweat a lot ! I won't give more details, I spent almost a month to find the adequate way to do that, mostly because at the start I had a basic knowledge of the frequency domain.

@laser : B&W films were easy to simulate compared to color ! I was not prepared to the dyes, and the couplers, etc. I am relying much on the manufacturers' data (curves, tech sheets), but many things are missing. I am also trying to stick the more I can to science (spectra, optics, energy, density, ...) --- But for the dyes and couplers part, for the first time in this project I think I'll have to approximate.

 

[Mr Bill]

I searched a little and I could get a scan of the SPSE Handbook of Photographic Science and Engineering, 1973. Is this the same book as the IS&T you are talking about, but an earlier version?

As koraks pointed out the main significance of the IS&T has been in the organization itself as well as the many technical conferences it has organized. It was originally known as SPSE, the Society of Photographic Scientists and Engineers. At some point, I'm thinking circa 1980, they changed the name to encompass other forms of imaging, thus the IS&T, the Society for Imaging Science and Technology.

Two handbooks were published, the first with the SPSE logo, the second, in 1997 I think, under the auspices of the IS&T. Both were extremely ambitious projects, and in certain circles were treated almost as an industry bible.

I was a 30-year-plus on-and-off member. Where I worked we always kept at least one person as a member to ensure an uninterrupted collection of the pertinent journals in our QC department. Not to mention sending one or two people to each such conference, to assure that we were in touch with the latest published research, and having the opportunity to chat with some of the researchers/authors. We were primarily a large processing lab, so our main interest was in photofinishing processes and technology, including silver recovery and effluent control, and that sort of thing. But it didn't just stop there.

Regarding the usefulness of past IS&T papers, I'd say that very few people on this site would find much direct use. But historically if you are a member you have access to the online papers. But not everything from a specific conference makes it there, so in certain cases it may be preferable to purchase a paper copy of the proceedings from said conference, IF still available).

 

[koraks]

Regarding the usefulness of past IS&T papers, I'd say that very few people on this site would find much direct use.

I agree, but this specific case is an exception. As I indicated before, most of the research underlying the kind of "print through analysis" @laser mentions was published in the IS&T journals. A lot of that work moreover dealt specifically with scanning in the motion picture domain, which was a major effort that Kodak invested significant time and effort into. It's somewhat ironic and disappointing that within the stills domain, it seems we are now in the process of reinventing the wheel. It's not just happening here, either. People esp. in the cultural heritage sector are presently working on this very topic and their approaches range from simplistic (and in some cases doomed to fail as they are based on erroneous assumptions) to comparable to what @AbsurdePhoton is trying to do, but more with an eye on digitization of collections and topics such as degradation of materials. What they seem to have in common is that none of them appears to be making use of the research output that's already there.

 

[Mr Bill]

People esp. in the cultural heritage sector are presently working on this very topic ...

Yes, an area where I don't have much background (nor interest, which I guess tends to go hand in hand). In such cases I think that a typical 3-color scanner is perhaps not good enough because the color makeup of "artifacts," or whatever one may call them, are "richer," for lack of a better word. So yes, in the IS&T library of published papers are studies using what they call "multi-spectral imaging." (Roy Berns of RIT is one that I recall being very into this sort of thing.) My superficial understanding of multi-spectral imaging is that it essentially takes more than the typical 3 color images; perhaps 6 or 8, for example. (This could be done, for example, with a monochrome sort of digital camera equipped with a filter turret and a set of carefully selected filters.) So the result would be somewhere between a 3-color scan and a more complete spectrophotometric scan.

With respect to color film scanning, I think that 3-color scanning is probably fine, provided that the 3 "colors" are a good match for the color film dyes. HOW to do it, exactly, is the big problem, and I don't recall any specific IS&T which would spell this out. I think the book by Giorgianni and Madden (I forget the exact title) sorta lays out the basic concepts, and would be a good starting point.

 

[koraks]

We're straying offtopic a little, but yes, there's indeed an active interest in multi-spectral imaging in the heritage/archival domain. Much of that has to do mostly with trying to as accurately as possible generate a digital facsimile of the original.

(Roy Berns of RIT is one that I recall being very into this sort of thing.)

Indeed, but not specifically in the film digitization domain. His research has revolved mostly, it seems, around reflective media. Although of course much of the theoretical underpinnings apply here as well.

But for the dyes and couplers part, for the first time in this project I think I'll have to approximate.

I wonder to what extent you must delve into this, really. I agree with @Lachlan Young that to a large extent you could consider the chemical package of the color film as a black box. All you seem to want to achieve is to be able to mathematically model the behavior of the film (again, pretty much as a black box) as it represents an original, real-world scene. This means that you'll naturally bunch together a massive number of parameters into a single algorithm to begin with, or at least that's how it appears to me.

densityTotal = densityYellow + densityMagenta + densityCyan + densityMin (the last one is what gives the developed film its orange hue, is this the "mask" you're all talking about ?

I skipped over this earlier, but the way you describe it here gives me the impression that you may be considering the orange mask as a fixed entity. Evidently, it's not - it's an image wise, variable mask. After all, that's what it's intended for - to compensate for imperfections in two of the three dye images and that compensation must naturally follow the dye density. However, also in this case I really doubt whether you need to take this into account at all, since could very well just assume that the whole film package acts as a simple input/output model with a certain distribution of spectral intensities going in, yielding a certain dye density output. (What we have not touched upon and what you seem not to yet pick up from the scanning discussion I hinted you at is the question what transmission spectra you would be keeping in mind in the first place; perhaps you're thinking of a theoretical/perfect-world/archetypal Red, Green and Blue - which of course in reality does not exist.)

 

[AbsurdePhoton]

densityTotal(λ) = densityYellow(λ) + densityMagenta(λ) + densityCyan(λ) + densityMin(λ) : it is for one discretized wavelength value (λ) - I have a system that can work at 1nm, 5nm or 10nm steps. So densityTotal is just a tiny bit of the whole. That's how I am including the min dye density. I then convert this spectrum using the CIE 1931 2° observer XYZ CMFs to XYZ values, then to linear RGB, then to simple RGB, the two last steps just for visualization, using an "observer" (CIE D65). That's how I obtain the negative image. In fact I am keeping the transmittance values that i feed to the printing part.
So for me yes the orange mask is sort of a fixed density that I combine (min dye density curve), am I wrong about that ? I first tried without it, and didn't get the orange mask. But it depends upon the type of dye curves : some are without the orange mask, others with it, they are often presented normalized, in fact they are all unusable as is, because this is a secret of the manufacturers. They're telling without giving all, often we just get the dyes middle gray and min curves.

In fact I was wondering today about the normalized curves, if I couldn't retro-engineer them. The peaks are clearly indicated by the dyes middle gray curve. I have the other curves, I know what type of status (M or A) was used to measure (it is precisely told in each technical sheet, and the process is described in the ISO publication 5-3, "Spectral conditions"). It is an optimization problem with multiple known variables that maybe I could resolve with Matlab.
There is also the solution to work with photos of color checkers, to find the formula to rectify the colors.
But this would have to be done for each film, and even each paper's dyes curves as well. A lot of work. I am wondering if I should just stick to the B&W simulation that works well.

 

[koraks]

That's how I am including the min dye density.

I see how you're including it, but not where it comes from. If you treat the orange mask as a constant and derive densityMin from e.g. a reading/simulation of an unexposed bit of film, then that's definitely a problem as it won't be accurate.

So for me yes the orange mask is sort of a fixed density that I combine (min dye density curve), am I wrong about that ?

Yes, that's incorrect.
And you're also correct that the HD curves are a stylized representation only and technically incomplete and incorrect.

The peaks are clearly indicated by the dyes middle gray curve.

I have a feeling you're now talking about either dye density curves or spectral sensitivity curves - probably the former? In the more expansive datasheets (e.g. Kodak) we can find a number of curves and it makes sense to make explicit what you're referring to:
* HD curves that describe density formed in relation to exposure light intensity
* Spectral sensitvity curves that describe how responsive the emulsion is to different wavelengths
* Spectral dye density curves that show what the spectral transmittance of the dyes are
These are sometimes augmented with additional curves w.r.t. granularity or MTF.
None of these curves can be assumed to be perfectly accurate or perfectly representative of measurements taken on a real-world piece of film.

But this would have to be done for each film, and even each paper's dyes curves as well. A lot of work.

Given the fact that each film product is unique, I think it's unavoidable that you end up doing a lot of work one way or another. An empirical approach involving test patches may even turn out to be the quick alternative to a much more time-consuming theoretical exercise. On the side of the paper, the good news is that the variety is much less if you focus on what's available on the market right now. Especially since Fuji's papers are basically all the same emulsion, just applied in different thicknesses, which results in fairly minor variations between products.

 

[AbsurdePhoton]

So for you, what would be the right way to include the orange mask ? I am a bit lost now.

 

[Lachlan Young]

So for you, what would be the right way to include the orange mask ? I am a bit lost now.

Are you trying to work from a film scan or a digital original? If the latter, adding the colour neg mask will make things less correct. The mask is there, as has been explained upthread several times, to correct for deficiencies in coupler formation in the shadows, but when exposed to paper with a 3200K source + 50R filtration (or equivalent RGB mix) it essentially presents a neutral but colour/ contrast corrected image.

As has been stated upthread by Bob Shanebrook (laser) a lot of the fundamental processes involved in making and analysing these materials are a lot more complex (especially once they begin to interplay at the coating/ layer build-up) than you are giving them credit for, and they cannot be particularly well simulated/ faked with just a bit of coding. People (and large corporations) have spent decades trying to find somewhat convincing film simulations and have persistently failed in the rather large gap between 'good enough' and 'convincing'.

Given the fact that each film product is unique, I think it's unavoidable that you end up doing a lot of work one way or another. An empirical approach involving test patches may even turn out to be the quick alternative to a much more time-consuming theoretical exercise. On the side of the paper, the good news is that the variety is much less if you focus on what's available on the market right now. Especially since Fuji's papers are basically all the same emulsion, just applied in different thicknesses, which results in fairly minor variations between products.

And even there, there are many complex aspects in terms of OTF/ MTF alone (never mind many other areas) that are immediately visually obvious when a direct optical print is made from the negative vs a scan & laser/ LED output on the same paper.

The thing that is also worth noting is that the cinema neg scan/ invert approaches can be a little more straightforward (exposures/ contrast ranges being, traditionally at least, more controlled at time of exposure). A lot of the rest seems to mainly be about 'fixing/ relighting in post'...

Having spent some time messing around with mask removal and inversion approaches, you often end up back at where Fuji's Frontier/ Image Intelligence mask/ colour correction routines landed (done well enough for anyone to not screw up the results vs perfect) with their habits of chopping off the ends of the scale to make it easier to correct consistently well without requiring more operator skill/ intervention.

 

[halfaman]

I agree that the best aspiration for an automatic color negative inversion is to be close enough to a usable result so it never requires a lot of intervention to put the image back on track. I don't know any software that nails the inversion with any film and any color balance, they all fail somewhere. You can try to choose how it fails.

Having spent some time messing around with mask removal and inversion approaches, you often end up back at where Fuji's Frontier/ Image Intelligence mask/ colour correction routines landed (done well enough for anyone to not screw up the results vs perfect) with their habits of chopping off the ends of the scale to make it easier to correct consistently well without requiring more operator skill/ intervention.

On the other hand,. Frontiers have the reputation of blocking shadows very easily, more than any other scan I have used (Epsons included). The actual tone range coming from my SP2500 turning off all post-processing corrections is really poor, you really need all the "magic" applied after the scanning to have something to work with.

 

[koraks]

So for you, what would be the right way to include the orange mask ? I am a bit lost now.

As I said, I wouldn't even bother trying to model how the film internally works. Just take it as a black box that turns spectral intensity of incoming light into spectral dye density.

 

[Lachlan Young]

On the other hand,. Frontiers have the reputation of blocking shadows very easily, more than any other scan I have used (Epsons included).

I could have said Noritsu as well. A lot of it has to do with fitting the outcome to the usable exposure range of the paper and the rest of the system is built to that end - and the end user is only allowed to get so deep into the process. Having seen jailbroken files off the Noritsu scanners, they are seemingly taking a pretty full range scan, then applying a fair bit of DSP before you can even get to the point of fiddling with them onboard the scanning software (again with the aim of protecting operators). Either way, it's interesting to see the what and why of the particular compromises baked into the black-box.

 

[AbsurdePhoton]

I find this all very discouraging... but I want to find out the more I can. Thanks for all this guys.

By the way, I found yesterday this project, similar to mine, but taking things a bit differently : https://github.com/andreavolpato/agx-emulsion
Some results look good, but I think there are too many shortcuts taken. One puzzling thing that I really didn't understand at all when I went to the wikipedia page : "the simulation of coupler inhibitors is inspired by Michaelis–Menten inhibition kinetics" - there's a linear inhibition formula.

What do you think of it ? His software is available and not too hard to install.

 

[koraks]

I find this all very discouraging... but I want to find out the more I can. Thanks for all this guys.

Well, nobody said this was going to be easy!

What do you think of it ?

As always, the question is what the purpose/intent is. It seems that the intent here is to be able to make an 'analog-like' version of a natively digital file. I'd have to see some examples to say anything useful. From a theoretical viewpoint, an inherent problem is that the workflow starts with a digital file that already represents some kind of transfer function of real-world spectral intensity into RGB values (even a RAW camera file is 'biased' so to speak). That's not really a problem if you just want to cook something up that looks a bit like an analog print, but it may be an issue if you're trying to simulate the whole process from a more technical viewpoint.

The whole thing keeps boiling down to what you're aiming for; in the first post you said:

I am trying to simulate analog films in a software

The question is at what point it's 'good enough' for your purpose.

I'd wager to say that at least the main gamma problem you had in the 'print without color filters' you showed in #1 seems to have been avoided or solved by the GitHub contributor you linked to.
Btw, I skipped over this bit earlier, but please note that a print made with a typical halogen light source enlarger without filtration, so C=Y=M=0 will look nothing like what you posted. I'm not sure whether this is a problem because...well, what's 'good enough', eh? Seems like that's still very much a moving target.

So perhaps start by making a little more specific (at least for the rest of us) what the desired end result would look like.