Calculating f-stop Timing in Enlarging

[Ian C]

Calculating f-stop Timing in Enlarging​

A number of threads on Photrio involve f-stop timing in enlarging. We’ve discussed dedicated f-stop timers, referencing the standard film-speed-number sequence, computed tables, time factors, and so forth. All of these can be useful. Another way to do this is to calculate the required time with a simple formula and an inexpensive calculator. The process is fast and easy. It can be more so by programming the formula into a calculator that allows it.

Whether you use a program or not, this allows you to try f-stop printing without the expense of an f-stop timer. If you find it sufficiently valuable, you might then decide to invest in an f-stop timer.

The following gives two useful formulas with examples for their use. The exposure times are rounded to the nearest 0.1 second.


Exposure Time for a Desired f-stop Change

If you made a print at t seconds and you want another to be Δ stops lighter or darker, the required exposure time is

(1) T = t*2^Δ

Where Δ is positive for a more exposure and Δ is negative for a less exposure.


Example 1. You’ve made a print at t = 17 seconds and you want to increase the exposure 0.4 stops. The new exposure time is

T = 17 seconds*2^0.4 = 22.4 seconds


Example 2. Your first print is 24 seconds, but you judge it to be 1/3 stop too dark. The required exposure time is

T = 24*2^(- 1/3) = 19 seconds


The Hewlett-Packard RPL code that accomplishes this is

<< 2 SWAP ^ * >>

The ordered argument list is: t, Δ


Calculate Burn/Dodge Time

(2) Burn/Dodge time = t*(2^Δ – 1)

Δ = the desired difference in f-stops (Δ is negative for dodging time).


Example: Suppose you’ve made a satisfactory 20-second print but want the sky 2/3-stop darker and an area in the foreground 1/2-stop lighter.

Burn(20 seconds, 2/3 stop) = 20 seconds*(2^(2.3) – 1) = 11.7 seconds.

Dodge(20 seconds, -1/2 stop) = 20 seconds*(2^(-1/2) – 1) = -5.9 seconds.


If you choose to program a calculator to automate the calculation, the Hewlett-Packard RPL code for burn/doge time is

<< 2 SWAP ^ 1 - * >>

The ordered argument list is: t, Δ

These HP programs work on models 28C, 28S, 48S, 48SX, 48G, 48G+, 48GX, and the 49 and 50 series calculators using RPL programing. The coding for other calculators is simple as well.


Burns and Dodges in Split-Grade Printing

We must consider the filtering system we’re using. When using Ilford Multigrade Filters, grades 4, 4.5 and 5 exposures require TWICE the exposure time of grades 00 – 3.5 to obtain the same effective exposure.

On the other hand, most, if not all, variable-contrast heads are designed to use the same exposure times at all grades. Check the owner’s manual of your unit for specific information to be sure.


Split Grade Using a Variable Contrast Head

Example: You’ve made a satisfactory work print at

Overall grade 0 exposure = 12 seconds

Overall grade 5 exposure = 10 seconds


After examining the work print you decide on the following changes:

At grade 0:

1. Dodge a small, overly dark area, by -1/3 stop.

Dodge(12 seconds, - 1/3 stop) = -2.5 seconds.


2. Burn all four edges 1/2 stop.

Burn(12 seconds, 1/2 stop) = 5 seconds.

3. Burn the left side 1/2 stop = 5 seconds.


At grade 5:

4. Increase the overall grade 5 exposure by 1/4 stop to increases the overall contrast.

T(10 seconds, 1/4 stop) = 11.9 seconds.

5. Burn a too-light bottom left area 1/3 stop, noting that the grade 5 overall exposure is now 11.9 seconds.

Burn(11.9 seconds, 1/3 stop) = 3.1 seconds.

Note: If you find any of these times impractically short, you can close the lens one stop to double the time.


Using Ilford Multigrade Filters

For simplicity, I’ll assume the same exposure times with the Multigrade filters as in the previous example using a VC head, except for the necessary 2X time increase using the grade 5 Multigrade filter. Thus, the overall exposures of the work print are 12 seconds at grade 0 and 20 seconds at grade 5.

At grade 0:

1. Dodge the small overly-dark area by -1/3 stop.

Dodge(12 seconds, -1/3 stop) = 2.5 seconds.

2. Burn all four edges 1/2 stop

Burn(12 seconds, 1/2 stop) = 5 seconds

3. Burn left side 1/2 stop = 5 seconds


At grade 5:

The grade 5 burn/dodge times must be multiplied by 2X due to the increased density of the Multigrade filters of grades 4, 4.5, and 5. Thus, the overall grade 5 exposure is initially 20 seconds

4. Increase the overall grade 5 exposure by 1/4 stop.

T(20 seconds, 1/4 stop) = 23.8 seconds.

5. Burn the too-light lower left area 1/3 stop, noting that the overall grade 5 exposure is now 23.8 seconds.

Burn(23.8 seconds, 1/3 stop) = 6.2 seconds.

 

[ic-racer]

I did the calculations for the most common factors, then use a simple calculator.

1/2 stop multiply or divide by 1.4
1/3 stop multiply or divide by 1.26
1/4 stop multiply or divide by 1.18

 

[Steve Goldstein]

Similar to what ic-racer does, I prestore various factors in my phone’s HP42 emulator (the app is called Free42) as follows:

1/2 stop in register 02
1/3 stop in register 03
1/4 stop in register 04
1/6 stop in register 06
1/12 stop in register 12
(There are more, but you get the idea…)

The pre-stored values allow me to quickly determine adjustments up or down. I know that much of my stored data are redundant - for example, 1/6 stop is the square root of 1/3 stop, 1/4 stop is the square root of 1/2 stop, etc. - but this redundancy requires less thinking, and besides, I’ve got 100 registers available.

BTW, Free42 is a great app but it’s not for everybody. It emulates an HP calculator so it uses RPN. This works for me but a lot of people have trouble getting the hang of a stack and chained operations. My first calculator was an HP41 so I grew up “speaking” RPN.

 

[pentaxuser]

Ian C ít looks as if * is the multiplication symbol, is it ?

What is the ^ symbol ?

Thanks

pentaxuser

 

[Chan Tran]

I would build the timer to work that way.

 

[Nicholas Lindan]

I use the EMU48 emulator for the 48GX, though I prefer to use the real thing. For android https://www.hpcalc.org/details/8987

It, and many more emulators are available from the hpcalc web site. hp calculator emulators appear to be a large cottage industry.

Of course, the emulators pale in comparison to a dedicated, integrated solution to the problem of f-stop timing calculation and control. Hint, hint.

ENTER > =

 

[Chan Tran]

I use the EMU48 emulator for the 48GX, though I prefer to use the real thing. For android https://www.hpcalc.org/details/8987

It, and many more emulators are available from the hpcalc web site. It seems hp calculator emulators are a large cottage industry.

ENTER > =

I use EMU48 a lot although I have both an HP48SX and HP48GX. The display on the real HP is too low in contrast especially the SX version. Very hard to see.

 

[Nicholas Lindan]

I use EMU48 a lot although I have both an HP48SX and HP48GX. The display on the real HP is too low in contrast especially the SX version. Very hard to see.

I agree, the SX display is horrid. My SX gave up the ghost and couldn't be fixed - the case is welded shut around a metal case that is itself welded shut. Not a good way to please your customers, no matter that it saved $0.25 in screws.

 

[Nicholas Lindan]

What is the ^ symbol ?

Exponentiation - "2 ^ 1.33" is 2 to the 1.33 power, though in hp-speak that would be "2 [ENTER] 1.33 [y^x]"

In Ian's "<< 2 SWAP ^ 1 - * >>" program the "^" stands in for the [y^x] key, SWAP for the [x<->y] key that swaps the x and y registers at the bottom of the stack and <<>> are the beginning and ending delimiters for a program. sort of like BEGIN/END; or {...}.

 

[RalphLambrecht]

Calculating f-stop Timing in Enlarging​

A number of threads on Photrio involve f-stop timing in enlarging. We’ve discussed dedicated f-stop timers, referencing the standard film-speed-number sequence, computed tables, time factors, and so forth. All of these can be useful. Another way to do this is to calculate the required time with a simple formula and an inexpensive calculator. The process is fast and easy. It can be more so by programming the formula into a calculator that allows it.

Whether you use a program or not, this allows you to try f-stop printing without the expense of an f-stop timer. If you find it sufficiently valuable, you might then decide to invest in an f-stop timer.

The following gives two useful formulas with examples for their use. The exposure times are rounded to the nearest 0.1 second.


Exposure Time for a Desired f-stop Change

If you made a print at t seconds and you want another to be Δ stops lighter or darker, the required exposure time is

(1) T = t*2^Δ

Where Δ is positive for a more exposure and Δ is negative for a less exposure.


Example 1. You’ve made a print at t = 17 seconds and you want to increase the exposure 0.4 stops. The new exposure time is

T = 17 seconds*2^0.4 = 22.4 seconds


Example 2. Your first print is 24 seconds, but you judge it to be 1/3 stop too dark. The required exposure time is

T = 24*2^(- 1/3) = 19 seconds


The Hewlett-Packard RPL code that accomplishes this is

<< 2 SWAP ^ * >>

The ordered argument list is: t, Δ


Calculate Burn/Dodge Time

(2) Burn/Dodge time = t*(2^Δ – 1)

Δ = the desired difference in f-stops (Δ is negative for dodging time).


Example: Suppose you’ve made a satisfactory 20-second print but want the sky 2/3-stop darker and an area in the foreground 1/2-stop lighter.

Burn(20 seconds, 2/3 stop) = 20 seconds*(2^(2.3) – 1) = 11.7 seconds.

Dodge(20 seconds, -1/2 stop) = 20 seconds*(2^(-1/2) – 1) = -5.9 seconds.


If you choose to program a calculator to automate the calculation, the Hewlett-Packard RPL code for burn/doge time is

<< 2 SWAP ^ 1 - * >>

The ordered argument list is: t, Δ

These HP programs work on models 28C, 28S, 48S, 48SX, 48G, 48G+, 48GX, and the 49 and 50 series calculators using RPL programing. The coding for other calculators is simple as well.


Burns and Dodges in Split-Grade Printing

We must consider the filtering system we’re using. When using Ilford Multigrade Filters, grades 4, 4.5 and 5 exposures require TWICE the exposure time of grades 00 – 3.5 to obtain the same effective exposure.

On the other hand, most, if not all, variable-contrast heads are designed to use the same exposure times at all grades. Check the owner’s manual of your unit for specific information to be sure.


Split Grade Using a Variable Contrast Head

Example: You’ve made a satisfactory work print at

Overall grade 0 exposure = 12 seconds

Overall grade 5 exposure = 10 seconds


After examining the work print you decide on the following changes:

At grade 0:

1. Dodge a small, overly dark area, by -1/3 stop.

Dodge(12 seconds, - 1/3 stop) = -2.5 seconds.


2. Burn all four edges 1/2 stop.

Burn(12 seconds, 1/2 stop) = 5 seconds.

3. Burn the left side 1/2 stop = 5 seconds.


At grade 5:

4. Increase the overall grade 5 exposure by 1/4 stop to increases the overall contrast.

T(10 seconds, 1/4 stop) = 11.9 seconds.

5. Burn a too-light bottom left area 1/3 stop, noting that the grade 5 overall exposure is now 11.9 seconds.

Burn(11.9 seconds, 1/3 stop) = 3.1 seconds.

Note: If you find any of these times impractically short, you can close the lens one stop to double the time.


Using Ilford Multigrade Filters

For simplicity, I’ll assume the same exposure times with the Multigrade filters as in the previous example using a VC head, except for the necessary 2X time increase using the grade 5 Multigrade filter. Thus, the overall exposures of the work print are 12 seconds at grade 0 and 20 seconds at grade 5.

At grade 0:

1. Dodge the small overly-dark area by -1/3 stop.

Dodge(12 seconds, -1/3 stop) = 2.5 seconds.

2. Burn all four edges 1/2 stop

Burn(12 seconds, 1/2 stop) = 5 seconds

3. Burn left side 1/2 stop = 5 seconds


At grade 5:

The grade 5 burn/dodge times must be multiplied by 2X due to the increased density of the Multigrade filters of grades 4, 4.5, and 5. Thus, the overall grade 5 exposure is initially 20 seconds

4. Increase the overall grade 5 exposure by 1/4 stop.

T(20 seconds, 1/4 stop) = 23.8 seconds.

5. Burn the too-light lower left area 1/3 stop, noting that the overall grade 5 exposure is now 23.8 seconds.

Burn(23.8 seconds, 1/3 stop) = 6.2 seconds.

I very much appreciate your efforts and your willingness to share, but I cannot see myself using a calculator in the darkroom during printing. That's where the dedicated f/stop timer comes in. It's a lot simpler to push one button to add or subtract 1/3 of a stop tan wipping the calculator out and do computations. However, it's probably helpful to gain a deeper understanding. Also consider all the help an f/stop timer can give for test strips and dodging and burning. To me, a dedicated f/stop timer is an irreplaceable tool in the darkroom that will quickly pay for itself in reducing frustration alone.

 

[Chan Tran]

I very much appreciate your efforts and your willingness to share, but I cannot see myself using a calculator in the darkroom during printing. That's where the dedicated f/stop timer comes in. It's a lot simpler to push one button to add or subtract 1/3 of a stop tan wipping the calculator out and do computations. However, it's probably helpful to gain a deeper understanding. Also consider all the help an f/stop timer can give for test strips and dodging and burning. To me, a dedicated f/stop timer is an irreplaceable tool in the darkroom that will quickly pay for itself in reducing frustration alone.

So this is what you use or you use a different model?

Darkroom Automation Fstop Timer

 

[pentaxuser]

Exponentiation - "2 ^ 1.33" is 2 to the 1.33 power, though in hp-speak that would be "2 [ENTER] 1.33 [y^x]"

Thanks I may be in the minority but I haven't done any maths that could not be done on paper or with a non scientific calculator since 1962 and such symbols are not part of my daíly life

I do now have a scientific calculator courtesy of a legacy from my son's schooldays and found the exponential button. A bit of playing around with it got me to the sequence for adding or subtracting stops

The intricacíes of Ian's programme are way beyond me

pentaxuser

 

[MattKing]

Thanks I may be in the minority but I haven't done any maths that could not be done on paper or with a non scientific calculator since 1962 and such symbols are not part of my daíly life

Just pull out your school days log tables from that drawer and you can easily do the calculations on paper too!
I can't remember for sure, but I think you can do them on a slide rule as well.

 

[Chan Tran]

Just pull out your school days log tables from that drawer and you can easily do the calculations on paper too!
I can't remember for sure, but I think you can do them on a slide rule as well.

When I was in junior high I stole a 7 digit log table from the library. I kept it for a long time. I don't know where it is now. It's something like a 500 page hard bound book.
Yes you can do it with the slide rule.

 

[Nicholas Lindan]

The intricacíes of Ian's programme are way beyond me

It only makes sense in the context of a late-model hp calculator.

hp calculators use a stack - think of it as a push-down stack of trays in the school cafeteria, except instead of trays this stack holds numbers. "+" in this context means add the top two numbers in the stack and leave the resulting number on the stack. The top of the stack is referred to as 'x', the number below it is 'y'.

The program << 2 SWAP ^ 1 - * >> is invoked with the number of seconds of the base exposure in the y position and the number of stops to burn in the x position. The steps in the 'program' are:

• Place the number 2 on the stack, on top of the number of stops to burn and the base exposure
• Swap the x and y numbers on the stack
• Raise y to the x power (y^x) - in this case raise 2 to the power of the number of stops to burn
• Place the number 1 on the stack, pushing down the contents of the stack
• Subtract the top number (equal to 1 in this case) from the next value on the stack (2^stops), leaving 2^stops - 1 on the stack
• Multiply the result by the base time
• This leaves the number of seconds to burn showing in the display as the contents of the top of the stck.

See, easy!

Bringing to mind Groucho Marx's comment in the movie Duck Soup. When presented with a government document Groucho exclaims: "Why this is simple, any 5-year old child could make sense of it. Quick, someone get me a 5-year old child, I can't make head or tail of it."

 

[Nicholas Lindan]

When I was in junior high I stole a 7 digit log table from the library.

A firm I worked for had a book of logarithms in the company library. It was Taylor's book; 1st edition; published 1792; the original thing from back in the day. They had it as a working reference book - "Good God, is anyone using this????" (*) I liberated the book. Over the years I have lost track of it, though I would not be surprised to find it in my basement. My heirs will likely come across it - "Good God. Did Nick actually use this????"

We're just a couple of log-table thieves.

(*) The standard reference was "CRC Standard Mathematical Tables and Formulae." The new edition does away with the table of logs - you are supposed to go to your calculator. A table of logs made sense in the pre-calculator days as a slide rule only provided precision to ~1%.

Logarithms rule! God never said "Go forth and add!" He said "Go forth and multiply!"

 

[Doremus Scudder]

Boy, this all looks so complicated!

I'll say it again: Using percentages instead of f-stop timing accomplishes exactly the same thing without that pesky square root of 2 and all the attendant calculations and decimals.

Yes, I know that light intensity works on the inverse square law and appreciate the physics and math behind all that, but I don't need to be bothered with any of that when printing.

Besides, there's really no constant density change with either f-stop timing or percentages for any given increment unless you always use the same paper at the same contrast setting. Every time you change contrast filtration, you change the density change per unit of time (that's the point, right?).

And, if you use any kind of split-grade dodging and burning, all bets are off.

I really fail to understand the appeal of making things more complicated in order to accomplish the exact same thing. Epicycles!

Doremus

 

[BobUK]

Thanks I may be in the minority but I haven't done any maths that could not be done on paper or with a non scientific calculator since 1962 and such symbols are not part of my daíly life

I do now have a scientific calculator courtesy of a legacy from my son's schooldays and found the exponential button. A bit of playing around with it got me to the sequence for adding or subtracting stops

The intricacíes of Ian's programme are way beyond me

pentaxuser

Just pull out your school days log tables from that drawer and you can easily do the calculations on paper too!
I can't remember for sure, but I think you can do them on a slide rule as well.

Our old math's teacher called slide rules guessing sticks.

During the first lock down I dug out my old log tables and slide rule, plus text books on the use of them.
I made more progress in a couple of days self education than I ever learnt in full time education.
Amazing what a person will do when boredom strikes. Or am I just a nerd?

 

[Chan Tran]

Boy, this all looks so complicated!

I'll say it again: Using percentages instead of f-stop timing accomplishes exactly the same thing without that pesky square root of 2 and all the attendant calculations and decimals.

Yes, I know that light intensity works on the inverse square law and appreciate the physics and math behind all that, but I don't need to be bothered with any of that when printing.



Doremus

Ian didn't say anything about square root of 2. He talked about 2 raised to the power of number of f stop change.
There is nothing about the inverse square law either.

 

[GregY]

Boy, this all looks so complicated!

I'll say it again: Using percentages instead of f-stop timing accomplishes exactly the same thing without that pesky square root of 2 and all the attendant calculations and decimals.

Yes, I know that light intensity works on the inverse square law and appreciate the physics and math behind all that, but I don't need to be bothered with any of that when printing.

Besides, there's really no constant density change with either f-stop timing or percentages for any given increment unless you always use the same paper at the same contrast setting. Every time you change contrast filtration, you change the density change per unit of time (that's the point, right?).

And, if you use any kind of split-grade dodging and burning, all bets are off.

I really fail to understand the appeal of making things more complicated in order to accomplish the exact same thing. Epicycles!

Doremus

I'm completely with you Doremus.

 

[RalphLambrecht]

So this is what you use or you use a different model?

Darkroom Automation Fstop Timer

This is a good model, but I use a model from RhDesigns.co.uk Both are a big help in the darkroom and have a strong following, but mine doesn't need a transformer to work with German electrical outlets, and it was developed by my co-author with minimal input from me.

 

[Alex Benjamin]

This is a good model, but I use a model from RhDesigns.co.uk Both are a big help in the darkroom and have a strong following, but mine doesn't need a transformer to work with German electrical outlets, and it was developed by my co-author with minimal input from me.

I have the StopClock Pro from RH Designs. It has changed my (photographic) life.

 

[Doremus Scudder]

Ian didn't say anything about square root of 2. He talked about 2 raised to the power of number of f stop change.
There is nothing about the inverse square law either.

I'm aware of that Still, Ian's method requires some calculations involving exponents to get to a desired new exposure. Works fine, but is needlessly complex in my view.

One flaw in all of this is that there is an unstated assumption that x-stops of exposure change will result in a proportional change in density. That simply is not the case unless the contrast filtration is the same and the paper is the same.

Every time you change contrast settings, the dynamic range of the paper changes. One stop difference in exposure with a #5 filter is a whole lot different change in density than one stop difference with a #1 filter. I find this difficult to reconcile with the whole premise of f-stop printing; i.e., that one can "know" somehow how many stops or fractions of a stop difference in exposure is needed to get the desired result just by looking at the first print. With split-grade printing methods, this would seem even more elusive.

Furthermore, wanting to deal with fractions of a second in exposure times seems superfluous as well. If a one-second change in exposure makes a noticeable difference in my prints, then my exposure time is way too short.

I like the idea of proportional exposure, so that density increases on test strips are even and so one can make an educated guess as to the next best exposure when making small exposure changes (when large exposure changes are needed it's always better just to make another test strip). And especially in recording dodging and burning so they can be easily calculated when scaling a print up or down. But, I don't think much more is needed to accomplish that than dividing the current exposure time by 10 (and maybe that by 2 if one wants a 5% change) and then working with multiples of that number.

Here's Ian's example for increasing a base exposure of 17 seconds by 0.4 stops: T = 17 seconds*2^0.4 = 22.4 seconds. To get this, you need a calculator with an exponent function or a slide rule (unless you can do decimal exponents in your head).

My method: increase exposure 30% (that's about 0.4 stops). 10% of 17 seconds is 1.7. Multiply that by 3 = 5.1 (I can do that in my head easily). Add that to the base exposure (also easy to do in my head) = 22.1 seconds. I'll ditch the tenth of a second and just expose 22 seconds. Voilà! No calculators or slide rules up my sleeves, no turning on lights to see displays and faster too.

Any visualization that one can do with increments in stops, one can do with percentages just as easily, but the same caveat applies; the density changes per unit are different at different contrast settings.

Best,

Doremus

 

[Nicholas Lindan]

There seems to be confusion between the math behind f-stop printing (logs and exponents) and f-stop printing itself.

f-stop printing with an f-stop timer requires no math whatsoever. Nada, zilch, kein, net, non, nei....

There is no more math involved in f-stop printing than there is in setting the shutter speed and aperture on a camera.

* * *
​

I'm sorry to say, but percentages just introduce unneeded complication.

Taking 15% of 17 seconds is not something I am going to do in my head in the middle of a printing session. Tapping the "^" key on an f-stop timer is something I can manage.

 

[Doremus Scudder]

Nicholas,
You're absolutely right! The catch is, you need that f-stop timer. For those of us who don't have the means or desire to invest in one of those, percentages are the next best thing.

I used a metronome to time my prints in the beginning. I had one because I'm a musician as well. It served double duty (I even developed film with it). Now that I have an inexpensive timer or two (used GraLab 450s), I still just set them to beep once a second and time from there.

For those that want an f-stop timer, I'd say, "go for it." For those of us who don't or can't, f-stop timing without an f-stop timer is pretty needlessly complicated (charts, calculators, etc.). Percentages offer a reasonable alternative.

Best,

Doremus