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Use GraCE
(currently this is an EXCEL
Spreadsheet)
Introduction to GraCE Introduction to GraCEGraCE is an Excel spreadsheet that provides two main functions:
It is useful to know the actual contrast range of a split grade print as this can help to inform the fine-tuning of the grade decisions. The inverse function provides a good starting point for the exposures needed to split-grade a print that has been worked to a point at a single grade. The second function also allows intermediate grade steps to be specified, calculating the appropriate split-grade exposures to achieve that intermediate step The calculations can be configured to cater for different material characteristics. The manufacturer’s quoted contrast range and ISO speed settings can be entered. The calculator is configured for Ilford MG IV RC™ across eleven full and half grade steps from 00 through 5. The number of configured steps can be altered to cater for the information available for different materials, although fewer steps will increase the burden on the extrapolations and reduce accuracy. Using GraCELayout of the spreadsheetThe spreadsheet is colour coded:
At the top of the sheet (rows 1 through 8) there are two areas for entering the function values and viewing the results. Column B is used to calculate the actual and nearest grades from the details of a split grade print. Column I is used to calculate the required split-grade to achieve a desired grade. At the left of the sheet, for convenience, an f/stop vs. time calculator is provided in columns L and M. The remainder of the sheet contains the configuration and intermediate results. Concepts, Rules for Value EntryThe sheet uses the concept of Major and Minor exposure steps. This is just a convenience to distinguish the two exposure steps of a split-grade operation. The Major step needn’t be the longest exposure. Usually in a split grade process the printer thinks in terms of a basic grade modified by a secondary exposure. In this thinking the Major step is the basic grade, and the modifying step is the Minor grade. To perform grade calculations the sheet uses exposure times. It is most natural to use actual exposure times, but this is not necessary – so long as the time base for all exposure details is constant. This means that times should be entered as though the f/stop used for both exposures was the same. If this wasn’t the case then the times must be adjusted, and the f/stop calculator is a convenient aid for this. Resulting exposure times assume the same time-base, i.e. f/stop value. In most cases grade values are entered as either whole or half-grade values. This is because Multigrade filter sets operate in whole and half grade steps, as do the controllers for typical Multigrade enlarger heads. The sheet does not use entered grade values directly, it conditions them into good values first. This ensures that impossible statements (such as using grade 7, or 3.1) do not upset the calculation engines look-up logic. The conditioning performed is:
The upshot of all this is almost any numeric value can be entered for a grade value and the sheet will make sense of it. The understood values can be seen in the cyan boxes adjacent to the grade entry fields. The calculations use value -1 for grade 00, but 00 or -1 can be entered. The ‘Desired Grade’ entry cell is an exception. Here we want to be able to enter intermediate grade values, since that is often the point of split-grade printing. So 4.1 is not rounded to 4, for example. Again grade 00 can be entered as 00 and this is converted to -1. However, just as it is possible to enter grade 4.25 (meaning halfway between grades 4 and 4.5) it is possible to enter 00.5 (meaning halfway between grade 00 and grade 0), which is converted to the understood value -0.5. Grades between 0 and 00 can either be entered as negative values between -1 and 0, or as fractions of 00 (00.25, 00.5, 00.6 etc). Actual and Nearest GradesThe actual grade of a split-grade print is calculated by entering the two exposure times used at each grade, as per the rules for grade and time entry discussed above. Cell B6 shows the actual grade of the resulting print. Cell B7 indicates the nearest grade that could be used in a single-grade print to achieve a similar result. Cell B8 shows the exposure time required at the nearest grade. Tonal values shift as a result of changing grade, some shifting up the scale and some shifting down the scale. Tonal values also shift as a result of changing exposure, but in this case all the values shift in the same direction, up or down. Any difference between the actual grade achieved and the nearest working grade can be compensated for, to an extent, by a minor exposure shift. If the actual is greater than the working contrast range then the working range is less steep than it should be, low values will not dip so far down the tonal scale and high values will not reach quite as far up the tonal scale. The low or the high values can be brought largely in line by adjusting the exposure. A little more exposure can bring the low values in line with the split-grade result; a little less exposure can bring the high values in line. The degree of workable exposure shift is given by the percentage difference between the actual and working contrast ranges. The exposure value in cell I13 shows the workable degree of shift in seconds. The following table summarises the use of this value:
And in the above table ‘a little’ is any amount up to that shown in cell I13. The sheet assumes that the split-grade print has been made in two steps. It is quite possible to split-grade over more steps, for example a grade two print may be given a little grade 5 to enhance the shadows and a little grade 0 to enhance the highlights. This case is not catered for in the current sheet. Grade Adjust By SplitCalculating the exposure steps needed to achieve a contrast grade using two exposure steps requires two sets of information:
To achieve a split-grade print two exposures are required, one of a higher grade than the desired result and one of a lower grade. If the entered Major and Minor grades to be used are both greater than the desired grade then the desired grade can not be achieved and the results will indicate ‘UErr’, meaning usage error. Similarly if both grades to be used are less than the desired grade. The desired grade and the grades to be used need not bear any relation to the starting grade. The starting grade is only used as basis for the exposure calculations. The exposures required at each of the two grades to be used to achieve the desired grade are shown in cells I7 and I8. These have been adjusted in line with the configured paper speed at each grade to be used and so are the actual times required. f/stop CalculationA time value can be entered in cell M2 and an f/stop selected in cell L2. The equivalent time at any f/stop can be read from the table below these entry cells. The table is arranged in ½-stop values. Because f/stops are never quoted in exact values cell L2 allows the f/stop to be selected from a list rather than typed in, this ensures an ‘understood’ f/stop value is used. For example, the actual whole-stop value between f/4 and f/8 is f/5.656, which mathematically is f/5.7. By convention that stop is referred to as f/5.6. Using raw mathematical values for the f/stop entry may have given more flexibility, but with a loss of convenience. Configuring The CalculatorThe sheet is pre-configured for Ilford Multigrade IV™ RC. The manufacturer’s data sheet supplies actual contrast ranges for whole grade steps only, so the half grade step contrast range values have been interpolated along a straight line joining the actual contrast ranges of the adjacent whole grade values. This is reasonably accurate as the contrast range versus grade is very nearly a straight line anyway. The contrast range values may vary between paper types and the actual values for the paper in use should be entered. A copy of the sheet should be created for each paper type in use. The paper speed at each grade can also be entered to configure the sheet, and again this should be available in the manufacturer’s data sheet. However, if grades are selected by an additive method such as with a dual light-source Multigrade head (as opposed to the subtractive nature of filtering) then the speed values can all be set to the same value – and in fact any value will do. Design and ConstructionThe CalculationsNearest Grade CalculationsThe nearest grade intermediate values are shown in rows 11 and 12. Firstly the actual contrast range and paper speed (ISO) are looked up for the Major and Minor grades used. The actual exposure time used for the minor grade is then adjusted in proportion to the paper speeds of the major and minor grades, so that the effective exposure of the minor grade is known. The effective exposures are shown in cells I11 and I12. From the effective exposures the percentage of the total exposure that each grade represents is calculated as the grade’s contribution. This is shown in cells H11 and H12. Row 13 then shows the calculated actual grade. First the actual contrast range is calculated by summing the percentage contribution of each exposure step’s contrast range. As an example:
Next, the actual contrast range is converted into an actual grade value. This is done by performing a straight-line interpolation. This is can be quite complicated, but there are two advantages with the approach:
Continuing the earlier example:
In row 14 the sheet then calculates the nearest working grade to the actual grade achieved from the split-grade. The nearest working contrast range is found by looking at the difference between the actual contrast range and the contrast ranges of the nearest greater and lower values in the configuration table. For an actual contrast range of 83.96 (as per the example) the possible working ranges are 75 or 90 (as per the configuration data). 83.96 is nearest to 90, and so that is taken as the nearest working contrast range. From the nearest working contrast range the associated grade value and paper speed is found by simple lookup. The required exposure at that grade is then calculated. First the sum of the effective exposures is calculated, this is the total exposure at the paper speed of the major grade. The working grade may be at a different speed so then the total effective exposure is proportioned appropriately. Next, the exposure adjustment value is calculated. The percentage variance between the actual and nearest working contrast range is found. The exposure adjustment value is that same percentage of the basic exposure value. To conclude the worked example:
Grade From Split CalculationsRow 19 contains the exposure time calibration values. The starting grade and exposure time are copied down from the entry area and the paper speed at the starting grade is looked up from the manufacturer’s data in the configuration table. This allows final exposure times to be determined. For completeness the starting grade’s contrast range is also looked-up, but this is not needed. Row 20 contains the calculations pertaining to the desired grade. The contrast range at the desired grade, which need not be a whole or half grade step, is interpolated. This is achieved in much the same way that the nearest grade interpolations are performed. The paper speed at the nearest grade is also looked up. This is somewhat arbitrary as paper speeds are discrete in nature. It isn’t actually possible to predict a paper speed for grade 3.2, however this value is used in normalising exposure times at different grades and is ultimately factored out. The starting exposure is proportioned by this nearest grade’s paper speed and the starting exposure’s paper speed. Rows 21 and 22 contain the calculations for the major and minor exposure steps. The grades to be used are brought down from the entry section and the contrast ranges and paper speeds at these grades are looked up in the configuration table. The contribution to the whole exposure that is required from each grade to achieve the desired grade is calculated by interpolating the position of the desired contrast range within the contrast range spread of the grades to be used. This is similar in nature to the interpolations used in the nearest grade calculations described earlier. The desired grade’s effective exposure is then split between the grades to be used in the proportions of the calculated contrast range contributions. These effective times are then proportioned by the (arbitrary) desired grade’s paper speed and the actual exposure step paper speed to give final actual exposure times for each exposure step. As an example:
Reviewing the above we can see that the major exposure is derived from
And clearly, the arbitrary Nearest Speed value factors out. f/stop CalculationsThe f/stop calculations are simple. First the entered time is inserted into the results table at the appropriate f/stop row. Successive rows following this point are then calculated as the previous row value multiplied by the square root of two. Successive rows prior to this point are calculated as the next row value divided by the square root of two.
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