I have a colour standard card QP 201 which I am hoping to use to calibrate gray values in some scientific photos. For this purpose I will need to know the percentage gray values of the gray squares (e.g. 18% gray, 95% gray), but the card does not come with that information. The closest that I can find is this chart - how do these RGB values correspond to percentages? Is it simply a linear transformation, so that 255 equals 100%, hence the corner squares (RGB 179, 180, 178) would be 70% gray?
Photography is approaching 200 years of age, first permanent image Joseph Niepce 1826. The digital era starts in 1975 when Steven Sasson at Kodak invented the first digital camera. In the early days, exactly how to expose and develop was hit and miss. It was Hurter & Driffield who conceived the science of Sensitometry. This is the science of how film and photo paper react to exposure and chemical developing. Thus applying numerical values to shades of gray or hues is rooted in this science. Their math is the basis of exposure calibration and film speed.
It’s a complicated subject because engineering of that era relies on logarithmic notation. This math notation, still used extensively, was the mainstay before engineers had electric calculators (computers). The slide rule was used every day for multiplication and division. Before the slide rule, books filled with tables were used. The basis of the tables and the slide rule is logarithmic notation. This math method substitutes addition for multiplication and subtraction for division. Its use permitted ships, buildings, airplanes, etc. to be designed with pen and paper. Photography also appreciated the use of logarithmic notation.
The increment of exposure is the f-stop. We open up or close down the circular opening of the aperture to control the light energy that plays on film or digital sensor. The f-stop adjustment changes the light energy of exposure in 2x increments, a doubling or halving of the exposing light energy. In modern cameras we often work in 1/2 or 1/3 f-stop increments.
Sensitometry (stemming from Hurter & Driffield) is the science of exposing film (now digital) using precise exposure changes, usually 1 stop or ½ f-stop. Typically a black & white film is exposed to make a gray scale --- clear film to max black. Each step is measured by passing a beam of light of known strength through the developed film. The amount of light blocked due to the density of each step is recorded. The results, called film density, is graphed on ruled paper. The result is a plot of the film’s response to exposure and development.
If the math used to record the density of each step is ordinary -- 10 base numbers, the graph is too long to be practical (several yards long). This is because each f-stop is a 2x change in exposure, so after fourteen steps, the scale is 8,192 the first step. To make the graph practical, some say elegant, logarithmic notation is used.
Sorry no time or space for a logarithmic lesson, but here is a taste of the math of photography:
T = Transmission the amount of light that gets through the film ÷ Amount of light that hit the film. A transmission of 18% means 18% of the light that hits gets through. Percent means per 100 so 18% in decimal form is 0.18.
O = Opacity the amount of light that hit ÷ Amount of light that gets through. O = 1/T we don’t use the word percentage thus 1 ÷ 0.18 = 5.56.
D = Density this value is the opacity in logarithmic form log(5.57) = 0.75
The key tone of photo film and paper is a gray patch with a density of 0.75 (log base 10). This is middle gray of the scale of film and photo print paper (battleship gray).
A patch of film with a density of 0.75 is the center value of the tonal range of a pictorial black & white negative (patch # 7 of photo below) A print made from this negative, properly exposed on photo paper and properly developed yields a gray patch, we say zone V, the pivotal point, and both properly exposed film and a print of that film have the same density. The film’s density is 0.75 transmission density, the print’s density is 0.75 reflected density. This is the value of the 18% gray card used to calibrate exposure meters.
Your example square is actually about 53%.
Upon reference image download exiftool shows that the ICC profile is ProPhoto RGB:
Kali:~ kelsolaar$ exiftool ***/rgbvalues.jpg ExifTool Version Number : 10.80 File Name : rgbvalues.jpg Directory : *** File Size : 316 kB File Modification Date/Time : 2019:09:08 14:06:30+12:00 File Access Date/Time : 2019:09:08 14:18:20+12:00 File Inode Change Date/Time : 2019:09:08 14:09:20+12:00 File Permissions : rw-r--r-- File Type : JPEG File Type Extension : jpg MIME Type : image/jpeg JFIF Version : 1.02 Exif Byte Order : Big-endian (Motorola, MM) Orientation : Horizontal (normal) X Resolution : 72 Y Resolution : 72 Resolution Unit : inches Software : Adobe Photoshop CS2 Macintosh Modify Date : 2007:09:12 11:12:29 Color Space : Uncalibrated Exif Image Width : 1742 Exif Image Height : 566 Compression : JPEG (old-style) Thumbnail Offset : 332 Thumbnail Length : 4057 Current IPTC Digest : 460cf28926b856dab09c01a1b0a79077 Application Record Version : 2 IPTC Digest : 460cf28926b856dab09c01a1b0a79077 Displayed Units X : inches Displayed Units Y : inches Print Style : Centered Print Position : 0 0 Print Scale : 1 Global Angle : 120 Global Altitude : 30 Copyright Flag : False URL List : Slices Group Name : ProPhoto Num Slices : 1 Pixel Aspect Ratio : 1 Photoshop Thumbnail : (Binary data 4057 bytes, use -b option to extract) Has Real Merged Data : Yes Writer Name : Adobe Photoshop Reader Name : Adobe Photoshop CS2 Photoshop Quality : 12 Photoshop Format : Progressive Progressive Scans : 3 Scans XMP Toolkit : 3.1.1-112 Format : image/jpeg Creator Tool : Adobe Photoshop CS2 Macintosh Create Date : 2007:09:12 11:12:29+02:00 Metadata Date : 2007:09:12 11:12:29+02:00 Document ID : uuid:1EB2585362B311DC9D2ADDF10FA72CD1 Instance ID : uuid:1EB2585462B311DC9D2ADDF10FA72CD1 Derived From Instance ID : uuid:1EB2585062B311DC9D2ADDF10FA72CD1 Derived From Document ID : uuid:4162C64161E811DC9D2ADDF10FA72CD1 Native Digest : 256,257,258,259,262,274,277,284,530,531,282,283,296,301,318,319,529,532,306,270,271,272,305,315,33432;80CC530BEFCFB6E95CD01DEF050420F7 Color Mode : RGB ICC Profile Name : ProPhoto RGB History : Profile CMM Type : Unknown (KCMS) Profile Version : 2.1.0 Profile Class : Display Device Profile Color Space Data : RGB Profile Connection Space : XYZ Profile Date Time : 1998:12:01 18:58:21 Profile File Signature : acsp Primary Platform : Microsoft Corporation CMM Flags : Not Embedded, Independent Device Manufacturer : Kodak Device Model : ROMM Device Attributes : Reflective, Glossy, Positive, Color Rendering Intent : ICC-Absolute Colorimetric Connection Space Illuminant : 0.9642 1 0.82487 Profile Creator : Kodak Profile ID : 0 Profile Copyright : Copyright (c) Eastman Kodak Company, 1999, all rights reserved. Profile Description : ProPhoto RGB Media White Point : 0.9642 1 0.82489 Red Tone Reproduction Curve : (Binary data 14 bytes, use -b option to extract) Green Tone Reproduction Curve : (Binary data 14 bytes, use -b option to extract) Blue Tone Reproduction Curve : (Binary data 14 bytes, use -b option to extract) Red Matrix Column : 0.79767 0.28804 0 Green Matrix Column : 0.13519 0.71188 0 Blue Matrix Column : 0.03134 9e-05 0.82491 Device Mfg Desc : KODAK Device Model Desc : Reference Output Medium Metric(ROMM) Make And Model : (Binary data 40 bytes, use -b option to extract) DCT Encode Version : 100 APP14 Flags 0 :  APP14 Flags 1 : (none) Color Transform : YCbCr Image Width : 1742 Image Height : 566 Encoding Process : Progressive DCT, Huffman coding Bits Per Sample : 8 Color Components : 3 Y Cb Cr Sub Sampling : YCbCr4:4:4 (1 1) Image Size : 1742x566 Megapixels : 0.986 Thumbnail Image : (Binary data 4057 bytes, use -b option to extract)
With that knowledge and Colour, it is possible to decode the values as given in your image and convert them to Luminance values which for practical purposes would be equivalent to reflectance values for the various gray swatches:
Kali:~ kelsolaar$ python Python 3.6.4 |Anaconda, Inc.| (default, Jan 16 2018, 12:04:33) [GCC 4.2.1 Compatible Clang 4.0.1 (tags/RELEASE_401/final)] on darwin Type "help", "copyright", "credits" or "license" for more information. >>> import colour >>> RGB = colour.models.eotf_ROMMRGB([179, 180, 178], in_int=True) >>> colour.models.RGB_luminance(RGB, colour.models.ROMM_RGB_COLOURSPACE.primaries, colour.models.ROMM_RGB_COLOURSPACE.whitepoint) * 100 53.26811741384234
I made a Google Colab notebook so that you don't need to install Colour on your machine: https://colab.research.google.com/drive/1OuaAnxqct3E4OAbddcA74vcNF4uwQyx4