As an example, we want to measure $f(t)$, but it's hard to get it directly. What we can do is to measure $f(t)-f(t-\tau)$. How to use the information we have to find $f(t)$?

The only method I know is, when $\tau$ is small enough, $$f(t)-f(t-\tau) \approx \tau f'(t)$$ then integrate it. But I still feel this is not good enough.

**Motivation**

We need to measure the instant frequency of a tuneable laser source (or the instant phase $\phi(t))$, and through swept-wavelength interferometer we get the beat signal $\cos(\phi(t)-\phi(t-\tau))$, where $\tau$ is the delay of two arms, so I'm struggling with dealing this issue. If any solutions here, please feel welcome to show your wisdom.