01 / using light to measure depth

revisit / light, phase & interference in a soap film

In the soap film, light reflected along two paths and the waves added. Here we arrange those paths deliberately: one visits the object, the other a known reference. Their phase difference becomes an intensity pattern. If we can recover that phase, we can measure how far light traveled.

For a narrow-spectrum source, a stable relative phase produces persistent bright and dark fringes. This stability is coherence. Move the relative phase below, then compare it with a phase that fluctuates during the camera exposure.

02 / how do optical paths become a height measurement?

A beam splitter sends light to the object and a reference mirror. Their returning waves meet at the camera. A difference in path changes their phase; interference makes that difference visible as bright and dark fringes.

In reflection in air, the light travels to the surface and back: a height change Δh changes the path by 2Δh.

03 / why does phase wrap?

Phase repeats every 2π. As the surface rises, the true phase keeps increasing, but the recovered angle returns to the interval −π to +π. The jump belongs to the representation, not necessarily to the surface.

Unwrapping counts the missing cycles by following a continuous phase field. Real steps, noise and undersampled fringes can make that count ambiguous. In reflection in air, an extra λ/2 of height adds a full phase cycle.

A camera can reveal hidden information when we change how light reaches it. Before returning to surface measurements, can we use light to see the air itself?

01 / how does schlieren reveal air?

When air density changes, its refractive index changes too. A density gradient bends light slightly. Collecting optics focus the light at a knife edge. Deflected rays shift the source image relative to the edge, changing how much light reaches the camera. Color schlieren uses a color-selective cutoff instead. We see optical evidence of the density variations, not the air molecules themselves.

A shock front produces a sharp change in the flow. Watch for a moving boundary in the optical view, then follow how the pattern evolves. Brightness and color are not a calibrated pressure map here.

02 / what does a picture leave out?

The optical sequence tells us where structures appear and how they move. Pressure sensors add a different measurement: pressure over time at their locations. Their combination is more informative than either alone, but we still need the setup, calibration and sensor positions before making quantitative claims.

play recordingplayback speed 1×2×4×8×

choose a frameWeb preview sampled from the original GIF. Playback speed is a viewing control; the time labels inside the recording describe the experiment.

play recordingplayback speed 1×2×4×8×

choose a frameWeb preview sampled from the original GIF. Playback speed is a viewing control; the time labels inside the recording describe the experiment.

03 / what keeps a wing up?

Around a lifting wing, the pressure distribution produces a net upward force and the airflow is deflected downward. Bernoulli relates speed and pressure in a simplified steady, low-speed flow. It helps interpret a known flow field; it does not determine that field by itself.

Use this form along a streamline with constant density, negligible viscous losses and height changes. It is not the equation for the shock front in the recordings above. Air parcels above and below a wing do not have to meet at the trailing edge at the same time.

04 / seeing is the start of measuring

Flow visualization turns an invisible event into something we can inspect. Schlieren, particle-based methods and interferometry reveal different quantities. The next post returns to surface shape: how can white light locate a surface rather than just show a pattern?

01 / what does coherence mean?

Temporal coherence describes how well a light field remains correlated with a delayed copy of itself. A narrow spectrum maintains that correlation over a longer optical-path difference. A broad spectrum loses it sooner.

Light often called “incoherent” can still interfere with a copy of itself when the delay is short enough. White-light interferometry uses this limited coherence. Spatial coherence is a separate requirement of the optical arrangement.

02 / how can an envelope maximum reveal depth?

A motorized stage moves the reference mirror to known positions. At every position, the camera records the intensity at every pixel. Move the stage manually or run a scan; each pixel stores the position where its envelope is strongest.

The mirror moves by Δz, but light travels that distance twice: the optical path difference changes by 2Δz. With broadband light, interference contrast is concentrated near equal optical paths. The maximum of the envelope identifies the depth of the selected point. Repeating this for every pixel maps the surface; a single fringe does not identify a unique position.

03 / what can we do with the measured surface?

A depth at every measured pixel gives a surface topography: steps, curvature and tiny changes in shape. What if those changes appeared after cutting a metal part?

01 / what changes when we cut a stressed part?

Cutting releases traction on the new surfaces. Under elastic relaxation, their tiny changes in shape contain information about the stress component normal to the cut.

02 / how does a surface become a stress map?

Align, mirror and average the two cut faces. Carefully smooth the contour, then use it to reconstruct the stress component normal to the cut.

The interferometer measures surface geometry. The contour method provides the mechanical reconstruction. Cutting quality, roughness and smoothing affect the result.

03 / why are small parts difficult to measure?

Roughness and measurement noise can obscure the small elastic relaxation. Their rapid spatial variations can also be amplified in the stress calculation.

04 / how do displacements become stresses?

In a linear elastic finite element model, we reverse the measured relaxation to restore the cut face to a plane. The stresses needed to do this reconstruct the original normal residual stress.

uₙ is displacement normal to the cut; ūₛ is the averaged, smoothed relaxation. The minus sign reverses that relaxation.

The model uses the specimen geometry, Young’s modulus and Poisson’s ratio, with constraints to prevent rigid-body motion. It assumes elastic relaxation during cutting.

05 / where does this become useful?

We now have the chain: measured surface → processed displacement → elastic model → normal stress. Next, we look more closely at the data-conditioning choices in that chain. Then we validate the method against a known stress field and investigate riser wires.

01 / noise depends on the question

In a measurement, noise is unwanted variability that obscures the quantity of interest. A vibration can be the signal when we study a structure, or a disturbance when it moves an optical setup. Noise need not be fast, random or acoustic; high frequency alone does not make something noise.

02 / optics & acoustics

In optical measurements, fluctuations in detected light and camera electronics can affect intensity and the phase we recover. In acoustic measurements, background sound and sensor electronics can obscure pressure or vibration. The mechanisms differ; the practical question is the same: how much of this record belongs to the response?

03 / precise, but accurate?

Each point is a repeated measurement; the center is the known reference. Precision describes how closely the measurements agree with one another. Accuracy describes closeness to the true value. A tight cluster away from the center is precise, but its measurements are systematically wrong.

Repeating and averaging can reduce independent random fluctuations. They do not correct a fixed systematic error. That requires investigating the instrument, method or calibration—the same distinction behind the fixed-offset control above.

04 / noise in human judgment

In Noise: A Flaw in Human Judgment, Daniel Kahneman, Olivier Sibony and Cass R. Sunstein examine unwanted variability in judgments that should agree. Bias shifts judgments systematically; noise makes them inconsistent. This is an analogy to measurement, not the same physical mechanism. A stable result can still be wrong, and a variable result needs more than a prettier curve.

05 / before reaching for a filter

First define the signal, inspect repeated records and check the instrument and environment. Reduce disturbances at the source when possible. Averaging and filtering answer different questions: one combines repeated observations; the other changes which variations remain in a record. The next draft explores when smoothing removes noise and when it removes useful shape.

01 / shape, texture or noise?

The recorded profile combines overall form, waviness, roughness and measurement errors. Cutting can add artifacts too. A rapid variation is not automatically noise: its meaning depends on the measurement and the engineering question.

02 / the same signal, two views

A profile shows where a variation occurs. Its frequency spectrum shows the scales of those variations. For a surface, we use position and spatial frequency (cycles/mm). For a time record, the equivalent axes are time and frequency (Hz). These are two views of the same data, not two different measurements.

03 / less noise, or less information?

Move the filter scale. A weak filter leaves fast oscillations. A strong filter also suppresses the smaller real feature. The useful setting preserves the relevant shape while reducing disturbances; it is not simply the smoothest curve.

04 / what did we do in the wire measurements?

Before smoothing, the two cut faces must be aligned, mirrored and averaged. Averaging cancels antisymmetric cutting effects, but symmetric artifacts can remain. Outliers and local cutting defects require separate inspection; smoothing is not a universal repair.

The smoothing choice propagates into the calculated stress. Compare stable features, edge behavior and uncertainty as the smoothing changes. The dissertation discusses selecting smoothing from the reconstructed stress response; no single setting works for every surface.

01 / from the whole riser to one wire

The pipe contains polymer and metal layers with different jobs. Tensile-armour wires wind around it in opposing helices, carrying axial loads. Manufacturing and forming can leave residual stresses before the riser ever enters service. Those stresses combine with the stresses produced by operational loads.

Flexible-pipe illustration reproduced from the supplied dissertation presentation; original credit: Journal of Petroleum Technology.

In my master's research, I combined scanning white-light interferometry with the contour method to measure this normal stress component in small wire cross-sections. The optical measurement supplies the relaxed surface shape; the elastic model supplies the stress. First, we check the method against a controlled bending test.

revisit / the contour method

02 / can the method recover a known bending profile?

revisit / conditioning measured data

A normalized steel bar (6 × 19 mm) was bent beyond yield and unloaded. We compare the measured residual stresses with the analytical bending profile.

After unloading, the remaining stress is the loading profile minus the elastic stress released. This subtraction produces the alternating tensile and compressive bands.

M is the applied bending moment, I the section’s second moment of area, and y the distance from the neutral axis. The loading profile includes yielding; My/I alone describes elastic bending, not the residual stress.

The alternating tensile and compressive bands are recovered. The experimental map is less uniform than the ideal prediction, especially near the edges. This is where the measured surface, cutting quality and data conditioning enter the result.

Averaged across the width, the measured stress follows the predicted sign changes. The uncertainty bounds show the limits of the reconstruction.

03 / what changes when the riser wire is formed?

Straight and curved riser wires show similar stress magnitudes but different distributions: forming redistributes stresses already present in the wire.

Experimental maps and curves retain their original numerical scales. Figure labels follow the selected language. Select a figure to enlarge it.

04 / what does this add to engineering decisions?

The measurements reveal a stress field that a photograph or the unloaded external shape cannot provide. Including that field can improve structural and fatigue assessments. It does not, on its own, predict a riser failure: operational loads, material behavior, corrosion, uncertainty and other failure mechanisms still matter.