How do I calibrate exposure to match a gray scale? EDIT: I need to clarify the question.

Kodak sells A gray scale card. It is used to calibrate B&amp;W filming. Film stock exposure is measured with a densitometer. If the film has been properly exposed and developed, each region of the card will register a specific density when measured with the densitometer.

This is different than a gray card. A gray card is used to adjust the exposure of a camera that has presumably already been calibrated, usually by the manufacturer.

Given the camera location and plane position in the blend file, it should be possible to set the lighting so that middle gray is properly exposed and then render. In the render, the luminance value of each patch should match that of the original image. This is similar to using a gray scale to calibrate a camera, but not exactly the same, but should be possible.

Is there some combination of color management settings that will accomplish this or do I have to use RGB curves to compensate?

(original question: I'm a black and white photography nerd. One of the things I've done with film cameras is to calibrate them to a grey scale card. I've tried this with no luck in Blender. With 50% gray properly focused, the values do not match the gray scale. How do I do this?

I'll attach a blend file with the lighting setups I've tried.

I've tried with three different lighting setups 
 - Remove the world lighting (set it black) and use a sun lamp pointing perpendicular to the image
 - Remove the world lighting and use an area lamp parallel to the image directly behind the camera
 - Remove the lights and use the world lighting.

In each case, I adjust the strength until the 50% value on the gray card shows a value of ~.5000 when a point in it is clicked in a render. I understand that there might be enough fall off from the area lamp that the card is not evenly lit, but for the sun lamp and the world light this should not be true.
I've tried this with various combination of color management parameters to no avail. The closest I've managed is filmic/raw, but it doesn't match a gray scale curve.)
To create a Gray Chart is quite easy:
Give the object a diffuse shader and set the albedo to 0.18 (Meaning a reflectance of 18%)

If you render the image and left click on the UV/Image editor, you can sample where the scene referred values are, and how those are being transformed into display referred values by the color transforms set in the color management section. (For blender 2.8 right click on the image and the sampler window will appear)

The numbers that move at the bottom of the screen are (From left to right) pixel coordinates, Z depth value, then Scene Referred RGBA values, Then the RGB values that follow the CM (CM stands for color managed) are the Display Referred values, those of your final image.

Sampling will help you determine how the light is affecting your scene and how those values are being transformed on the final image.
So how are the scene referred values being transformed to display referred ones? It all depends on the settings on the color management.
For filmic blender, mid gray would be a scene referred value of 0.18, and it would get mapped to a value of 0.5 in display referred values. (sRGB tends to end up with display referred 0.5 at around 0.2 scene Referred)
If you are using Filmic Log encoding in as your view transform, you can also enable the False Colour Look. That will give you an interactive way to judge the &quot;exposure&quot; of your scene. Mid gray (in display referred values) will show as gray. Darker areas will be represented as blueish-purple and black, and bright areas as red, and eventually white once the values are too large.

Note that false colour should only be used with the filmic blender log encoding views. Using other view transforms will not result in an accurate representation.
For more details read the github page of blender render: https://github.com/sobotka/filmic-blender
So the same basic cube would look something like this in false colour:

Another example:
This scene (the cube is set with a reflectance of 18%):

Woulld look like this in false colour.

To understand how filmic blender works read:
Render with a wider dynamic range in cycles to produce photorealistic looking images