A better understanding of temporal contrast in dynamic speckle

A new version of Van Gogh’s Starry Night?

But what is it, really? A new version of Van Gogh’s Starry Night?

Not quite. What you’re looking at is a rotating disk analyzed using a technique known as dynamic speckle imaging.

What Is Temporal Speckle Contrast?

Dynamic speckle imaging allows us to extract motion-related information from a sequence of speckle images — random granular interference patterns generated when coherent laser light is scattered by a complex surface or volume.

The physical principle is fairly intuitive: when a rough or irregular object is illuminated with a laser beam, the multiple coherent reflections interfere and form what we call a speckle pattern.

Now, imagine that the microstructures within the object move slightly during the camera’s exposure time. That motion introduces blur into the speckle pattern. To quantify this blur, we use a robust metric: the speckle contrast, typically defined as the ratio of the standard deviation to the mean of the recorded intensity.

The faster the movement, the more blurred the speckle becomes — and the lower the contrast.

Two Ways to Measure Contrast

There are two main approaches to computing speckle contrast:

• Temporal contrast: track the intensity of a single pixel across time;
• Spatial contrast: compute the contrast across a neighborhood of pixels at a given moment.

In most applications, the temporal approach is preferred. It preserves spatial resolution and is widely used in biomedical imaging, for example to visualize blood flow.

Under certain assumptions — especially ergodicity and negligible additive noise — the speckle contrast can be related to the decorrelation time of the underlying electric field:

• Fast motion → fast decorrelation → low contrast.
• Slow motion → slow decorrelation → high contrast.

But Can Contrast Grow Indefinitely?

At first glance, it might seem that reducing motion indefinitely should lead to ever-increasing contrast. But this overlooks a subtlety.

If the motion becomes quasi-static, then the speckle pattern no longer changes across frames. Each image is identical, leading to zero variation over time — and therefore, zero temporal contrast.

This leads to a key insight:
The contrast does not grow monotonically with decreasing speed. Instead, it reaches a maximum at an intermediate velocity, then decreases again as the system approaches full stasis.

We’ve nicknamed this non-monotonic behavior the “hump curve.”

Why Standard Models Fail

Why doesn’t the usual theoretical framework predict this?

Because it implicitly assumes that successive frames are statistically independent — that is, fully decorrelated. But when motion slows down, this assumption breaks down.

At that point, ergodicity fails: temporal statistics no longer match spatial ones. Temporal contrast can no longer be treated as equivalent to spatial contrast.

Experimental Validation

To test this hypothesis, we designed a controlled experiment.

We mounted a rough metallic diffuser on a high-precision rotary motor, allowing us to vary both the disk’s radius and angular velocity. This setup enabled us to probe a wide range of tangential velocities.

And the results were striking:

• At low speeds, the contrast increases with radial distance — i.e., with speed — exactly as expected.
• But after a certain threshold, the trend reverses. The center, initially darker, becomes brighter than the edges.

Three Observed Regimes

We observed three temporal contrast regimes:

1. Frozen regime: speckle patterns are static across frames → zero contrast
2. Transitional regime: partial decorrelation between frames → rapid contrast increase.
3. Blurring regime: speckle grains are highly blurred → contrast decreases again.

Among these, the transitional regime is the most problematic:
It is neither fully frozen nor fully decorrelated, making the contrast evolution ambiguous and unreliable for quantitative analysis.

Final Takeaways

Our experiments confirmed that:

• In the growth phase (slow motion), the contrast curve depends primarily on the repetition time. This parameter must be carefully calibrated when studying very slow dynamics or tracking frozen speckle evolution.
• In the decay phase (faster motion), the contrast is dominated by the exposure time. Once frames are fully decorrelated, it is the exposure duration that governs the amount of speckle blurring observed.

This improved understanding of temporal contrast dynamics not only challenges traditional assumptions but also opens the door to better experimental protocols for measuring slow motions with high sensitivity.

The full paper discussed in this post is available as a preprint on:
Experimental Classification of Dynamic Speckle Regimes: Insights from Controlled Rotational Diffuser Measurements