A sensor fitted to a blender does not measure your batch. It measures a few milligrams of powder. And that figure is itself a calculation rather than a guarantee.
A content curve settles, the operation is stopped; three days later a uniformity check comes out at the edge of specification. The sensor was telling the truth, about different material.
This page gives the calculation of the mass actually seen at each acquisition, and what it leaves open.
The European Pharmacopoeia says the same: the portion tested in line is “usually smaller than a conventional sample”, and the scale of scrutiny must be considered (Ph. Eur. 5.25).
The calculation holds in one line
The mass probed by a diffuse reflection measurement is the illuminated volume multiplied by the bulk density of the product. That volume is a disc, the light spot, multiplied by the explored depth.
Probed mass = π r² × bulk density × explored depth.
With a spot radius of 2.5 mm, a powder at 0.38 g/cm³ and a depth of one millimetre, the result is about 7.5 mg, and 30 mg for a 10 mm spot. Set that against the tens or hundreds of kilograms the vessel holds.
Keep the order of magnitude: a few milligrams. A spectroscopic measurement is an elementary increment, not an examination of the batch. The answer is not a bigger sensor: it is more increments, which chapter 2.9.47 of the European Pharmacopoeia organises for content uniformity.
That figure is a calculation, with its assumptions
No manufacturer guarantees a probed mass, and that is logical: two of the three terms belong to your product and your process rather than to the instrument.
| Term | Where it comes from | Is it stable? |
|---|---|---|
| Spot radius | Optical design of the probe and working distance | Yes, as long as the installation geometry is respected. The one term really under control |
| Bulk density | The product, its packing, its moisture, the stress the equipment applies to the bed | No. It changes between the start and the end of a blend, between a full hopper and one at the end of discharge, between two raw material batches |
| Explored depth | The interaction between the radiation and the scattering medium | No. And it carries no fixed value that could be measured once and for all |
Direct consequence: the mass really probed is itself a random variable of the process. It fluctuates during the operation you are following. The 7.5 mg are a design order of magnitude rather than a calibration constant.
Penetration depth is a property of your material
People look for the penetration depth of NIR in a powder as they would look for a physical constant. It works differently.
Two mechanisms overlap. The radiation penetrates inside the particles, and it penetrates the bulk, travelling from particle to particle by successive scattering. Their relative weight follows the medium, and the factors that move the result are known.
- Particle hardness, which governs the fate of the light at each encounter.
- Particle size: a bed of fines and a bed of granules scatter differently.
- Bulk density, which therefore enters twice, as an explicit factor and by modifying the depth itself.
- Composition, each constituent carrying its own absorption bands.
- Wavelength: the explored depth varies from one end of the spectral range to the other. Short wavelengths generally penetrate further, because high-order overtones absorb far less than combination bands. Scattering works the other way and bounds the gain.
That depth is bounded experimentally, though. Varying the thickness of the bed until the spectrum stops changing gives the value that holds for your product in your configuration. A simple experiment, and it gives the value specific to your product.
The millimetre in the calculation is an assumption
The 1.0 mm used above is a calculation assumption. It gives an order of magnitude and comes from no measurement on your product. Penetration depth depends on the product as much as on the instrument: it is determined on your material, and it can move during a design of experiments or during a process as packing and particle size evolve.
What the formula lets you calculate
The formula goes as r squared. That dependence on the square of the radius is good news: the hardware answers are calculable, and their effect is fast.
A spot twice as wide probes four times the mass
Doubling the diameter of the spot multiplies the illuminated surface by four, and so the mass analysed at equal depth and packing. The most direct lever, and it is decided at the design of the installation.
A seven-point probe probes seven times the surface per acquisition
Spreading several spots over one acquisition multiplies the interrogated surface accordingly. And that surface is spread in space rather than concentrated on one place of the bed.
Both statements are calculations with their assumptions rather than manufacturer specifications: they assume the same explored depth and the same packing in the two configurations compared.
Your NIR only sees the surface
That is the classic objection, and it is accurate. A diffuse reflection measurement interrogates a few milligrams near the surface of the bed, and the manufacturers’ technical notes document it in black and white.
The answer sits elsewhere: build an explicit sampling strategy. Since an acquisition is an elementary increment, the useful question becomes how many increments, taken where, at what moment, aggregated how. That belongs to sampling theory, and a great deal of ground is gained there with no change to the instrument. On the cases where this question decides, we work with Kim Esbensen, an expert in our network. Sampling and representativeness.
A third route exists, playing on different parameters: enlarging the interrogated surface until it becomes an image. A camera sees the whole field rather than probing a few milligrams at one point, at the price of seeing the surface and of a noisier value per pixel than an averaged spectrum. The trade-off moves rather than disappearing. What imaging brings on this point, and what it costs.
What is worth preparing on your side
- The bulk density of your product, and where possible its range of variation during the operation.
- The mass of the dosage unit, tablet, capsule or dose: it is what says whether a few milligrams probed are relevant.
- The installation geometry, working distance, probe angle, window: a few millimetres of difference change the spot, and so the mass.
- The target content. The lower it is, the larger the mass to probe for an increment to mean something. A property of sampling, independent of the technology.
- The behaviour of the bed in front of the sensor, flowing, at rest, or packed against a wall: the same instrument probes a different mass in the three cases.
- Fouling of the window, and what detects it: a gradual deposit shifts the measurement without ever interrupting it.
This list is more than good practice. For an on-line measurement — and the EMA NIR guideline names determination of blend homogeneity explicitly — the submission has four points to address: optimisation of the sampling device location, estimation of the effective sample size, assurance that the window stays covered with sample, and controls against fouling. § 4.2.1. The calculation on this page is a submission deliverable, not an exercise.
Conditions for success and limits
Repeating the measurement at the same place reduces noise
Averaging ten acquisitions on the same portion of powder only reduces instrument noise. The uncertainty on the batch does not move, because those ten acquisitions speak about the same few milligrams. To gain representativeness, you have to measure several portions: a question of measurement design, not of signal processing.
A variable probed mass shapes how a dispersion is read
If packing changes during the operation, the mass analysed changes too, and the expected variability between successive portions with it. A decreasing dispersion can signal real homogenisation. Or progressive packing of the bed in front of the window. Telling them apart calls for following the spectral residuals, not only the predicted value.
Three situations where another route answers better
- A product very heterogeneous at the scale of the probed volume.
- A content so low that a few milligrams cannot establish anything statistically.
- An access point that only exposes stagnant product.
No instrument changes that. The question can, however, be moved. A measurement point downstream where the product flows, a multipoint probe, a transmission measurement on the dosage unit, or a move to an image: four routes that stay open. Working them up calls for trials, at a cost out of all proportion to that of an installation whose routine performance remains to be established. What makes a measurement hold.
What it changes in practice
Making this calculation before choosing an instrument changes the nature of the discussion. You then compare interrogated masses and sampling plans. Spot size and number of points become design variables.
The file gains too: a written and justified sampling strategy holds up to an auditor’s question. An undemonstrated claim of representativeness does not.
The calculation is made from your own figures, at the scoping stage. It sometimes concludes that the probed mass is small for the question asked and that another route answers better: a downstream measurement point, another geometry, another technology. That is a useful answer.
Frequently asked questions
Does the 7.5 mg figure apply to my product?
Only by coincidence. It corresponds to a spot of 5 mm diameter, a bulk density of 0.38 g/cm³ and an assumed depth of one millimetre. Change one of those three terms and the result changes. What to take away is the order of magnitude, and the method for recalculating with your own figures.
Can the penetration depth be measured on our own product?
It can be approached, for instance by varying the thickness of the bed until the spectrum stops changing. That holds for a given configuration rather than giving a constant. The same product more tightly packed, or after a change of particle size, gives another value.
Does a transmission measurement settle the problem?
It moves it favourably for a unitary object. Traversing a tablet interrogates its whole thickness, which is exactly what you want when the stake is the dose. In return it calls for constant geometry and thickness, and it does not apply to a powder bed in a vessel. Reflection and transmission compared.
Does a more sensitive detector increase the mass analysed?
No. The mass analysed is set by the optical geometry and by the product. A better detector improves the signal to noise of an acquisition, which is worth having, and it interrogates exactly the same material. The two quantities are independent, and confusing them is a frequent error in instrument comparisons.
How many measurements does characterising a batch take then?
It follows the real variability of the product and the precision sought on the mean. That is a sampling plan calculation. An in-line measurement produces increments in very large numbers, which no manual sampling allows, provided they are taken at instants and places that vary. How many samples it takes.
Give us three figures and you will know what your sensor is looking at.
The bulk density of your product, the mass of your dosage unit and the target content: enough to know whether a reflection measurement interrogates a relevant quantity, which spot diameter to aim for, and how many increments to aggregate. Forty-five minutes is enough.