Optical coherence tomography, usually abbreviated as OCT, is an imaging technique based on low-coherence interferometry.
It can produce depth-resolved information from weakly reflecting structures inside semi-transparent materials such as biological tissue.
The most common textbook picture is a Michelson-type interferometer in which light from a broadband source is split into a reference arm and a sample arm.
Reflections returning from the sample interfere with the reference beam only when their optical path lengths are closely matched.
This matching condition is called coherence gating, and it is what gives OCT its axial depth selectivity.
A key quantity in OCT is the axial resolution.
In this simulator, the prompt specifies the simplified relation
\[
\Delta z=\frac{\lambda_0^2}{2\Delta\lambda},
\]
where \(\lambda_0\) is the center wavelength of the source and \(\Delta\lambda\) is its bandwidth.
This formula captures the main physical trend: a broader spectrum gives a shorter coherence length and therefore a better axial resolution.
In other words, broadband light improves the ability to distinguish nearby reflecting layers in depth.
For the sample values
\(\lambda_0=1300\,\text{nm}\)
and
\(\Delta\lambda=100\,\text{nm}\),
the resolution is
\[
\Delta z=\frac{1300^2}{2\cdot100}\,\text{nm}=8450\,\text{nm}=8.45\,\mu\text{m}.
\]
This is exactly the sample result in the prompt.
The physical interpretation is that depth features separated by a distance clearly larger than about
\(8.45\,\mu\text{m}\)
can be distinguished more easily in the idealized A-scan.
In a simple OCT model, each reflecting interface in the sample contributes a peak in the depth profile.
If a layer at depth
\(z_i\)
has reflectivity
\(r_i\),
then an educational A-scan model can be written as a sum of localized peaks:
\[
A(z)\approx \sum_i r_i
\exp\!\left[-4\ln2\left(\frac{z-z_i}{\Delta z}\right)^2\right].
\]
This Gaussian form is not a full OCT signal derivation, but it is very useful because it connects the coherence-gating width directly to the depth resolution.
Each layer appears as a peak centered at its depth, and the peak width is controlled by the axial resolution.
The simulator uses a two-layer tissue model because that is a natural starting point for understanding OCT.
If the two layers are well separated compared with
\(\Delta z\),
the A-scan shows two distinct peaks.
If they are too close together, the peaks overlap and the structures become harder to resolve.
This is why source bandwidth is so important in OCT system design.
Another central concept is the coherence envelope.
As the reference path is scanned, only sample reflections that match the reference delay within the source coherence width interfere strongly.
In the simulator, this is visualized as a moving gate through the sample depth.
When the gate passes through a reflective layer, the detector signal rises and produces a peak in the A-scan.
This is the essence of time-domain OCT.
In real systems, additional details matter.
Tissue refractive index changes the relationship between optical path and physical depth.
Spectral shape changes the exact axial point-spread function.
Dispersion broadening, multiple scattering, and noise also affect the measured signal.
Modern systems often use Fourier-domain OCT, where the interference spectrum is measured and numerically transformed into depth information, rather than mechanically scanning the reference arm.
But the basic physics remains the same: low-coherence interference isolates reflections from specific depths.
At a more advanced university level, one studies k-space sampling, dispersion compensation, sensitivity roll-off, complex analytic signals, and the relation between source spectrum and axial point-spread function.
Even so, the introductory model already captures the main lesson:
broader bandwidth improves depth resolution, and sample interfaces appear as peaks in the coherence-gated depth scan.
\[
\Delta z=\frac{\lambda_0^2}{2\Delta\lambda},
\qquad
A(z)\approx \sum_i r_i
\exp\!\left[-4\ln2\left(\frac{z-z_i}{\Delta z}\right)^2\right].
\]
These formulas explain why OCT can perform micrometer-scale depth sectioning and why low-coherence interferometry is so powerful for retinal imaging, tissue diagnostics, and other biomedical applications.
