The term, "Roast Degree" pertains to how far along in the roasting process, a batch of roasted coffee beans are. 

Although there are a number of physical and chemical changes that occur during the roasting process, the easiest and most practical way to gauge how far along in the roasting process they are, is by measuring the color of the roasted coffee.

It has been well documented that higher temperature, and shorter term roasts, will yield roasted beans with larger bean size, as well as an increase in the number and size of pores. The inside color may also be different than the outside color. Because of this, it is generally recommended to measure roasted coffee in the ground state.
COFFEE COLOR AND ROAST DEGREE
There are a number of different methods, and instruments available, that measure color effectively. If you are roasting for your own customers, a simple color chart may suffice. However, if you are private label roasting and blending coffee, or if you have multiple roasting facilities, you will probably find it necessary to assign a numerical designation to the degree of roast, in which case a color analyzer with repeatable performance, will be required.  

Coffee color standardization testing, at least initially, was carried out using Agtron Spectrophotometers. Now there are a number of methods available, using technologies like laser, NIR, and digital imaging.
COLORTRACK LASER ANALYZER
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MOISTURE, PARTICLE CHARACTERIZATION, COLOR, AND SAMPLING
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PRODUCT CATALOGUE
SAMPLER CATALOGUE
Here, a real time laser color analyzer is pointed towards the viewing window, where the beam
monitors the coffee bean color inside the machine, while roasting.
LIGHTELLS NIR PHOTOMETER
DIGITAL IMAGING SOFTWARE (RGB)
RELATIVELY INEXPENSIVE, BUT  ACCURATE. SEE SCAA STANDARD
READS COLOR USING RGB VALUES. ALSO CAN BE USED FOR GRADING COFFEE BEAN SIZE, AND CALCULATING ACTUAL BEAN DENSITY.
CONNECTS TO A STANDARD SCANNER
MODIFIED REAL TIME LASER SHADE ANALYZER
COLLECTS 200,000 READINGS IN 20 SECONDS.
SEE SCAA STANDARD