02 Imaging

Optical density

OD = log₁₀(I₀ / I). A factor-of-10 drop in transmission is one OD unit.

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Simulation

Optical density — Change the numbers; the scene follows.

Where it works

Radiography room

Bucky / detector

In the Bucky / detector: grid, AEC, DQE, and the pixel that samples the image.

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Formula

\mathrm{OD}=\log_{10}(I_0/I)

Variables

I₀ · Incident intensityI · Transmitted intensity

Results

OD
Optical density
1.301
I/I₀
Transmission
0.05

Explanation

\mathrm{OD}=\log_{10}(I_0/I)

What it means

Film (and now some display QC) uses logarithmic optical density so that equal perceptual steps are equal OD steps. Base+fog ≈ 0.15–0.20, a chest film mid-grey ≈ 1.2, a black border ≈ 3. H&D characteristic curves plot OD versus log exposure. A 0.3 OD change is a factor of 2 in transmission — coincidentally one doubling of exposure in the linear portion of a film curve (γ ≈ 1). This is a working relation in Diagnostic imaging.

Where it is used

Clinically it sits on the Radiography room — Bucky / detector. In the Bucky / detector: grid, AEC, DQE, and the pixel that samples the image. Diagnostic equations live on the tube, the detector, and the patient: magnification, air kerma, CTDI, and why bone lights up at 70 kV. They turn a technique chart into physics you can defend.

Radiography room · Open this machine

How to use it

Enter incident and transmitted intensity (arbitrary units). OD 1 = 10% transmission, OD 2 = 1%, OD 3 = 0.1%. Change one input and watch the curve and the simulation follow.

Symbols

I₀Incident intensity100
ITransmitted intensity5

Worked example

A typical case from the default values: I₀ = 100 (Incident intensity); I = 5 (Transmitted intensity). Substituting into the relation gives OD = 1.301; I/I₀ = 0.05. These are teaching numbers — align them with your machine.

Typical values give

OD = 1.301
I/I₀ = 0.05

Where it comes from

The displayed formula is the working relation. OD = log₁₀(I₀ / I). A factor-of-10 drop in transmission is one OD unit. Usual reference: Bushberg / film sensitometry. Derive it in the specialty lesson, then return here to pin the numbers.

Reference: Bushberg / film sensitometry

Assumptions & limits

Incoherent visible light through a film or a printed step wedge. Not a CT number and not a linear grey value of a DR for-processing image (those use a vendor LUT).

Pitfalls

kVp is not the same as effective energy. CTDI is not patient dose — SSDE and organ dose come after. Do not quote DLP as if it were effective dose without a k-factor. Incoherent visible light through a film or a printed step wedge. Not a CT number and not a linear grey value of a DR for-processing image (those use a vendor LUT).

Keep this

Technique is physics: kV sets contrast, mAs sets noise, filtration sets the spectrum. Incoherent visible light through a film or a printed step wedge. Not a CT number and not a linear grey value of a DR for-processing image (those use a vendor LUT).

In this specialty

Diagnostic imaging