---
title: "Gravitational-wave lensing and frequency fringes"
description: "Follow one chirp along two paths around a mass, derive the point-lens amplification, recompute it independently and read the O3 lensing search."
canonical_url: "https://sandboxphysics.com/stories/gravitational-wave-lensing/"
language: "en"
page_type: "story"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/stories/gravitational-wave-lensing/"
last_modified: "2026-11-14"
---

# Gravitational-wave lensing and frequency fringes

Sandbox Physics · 2026-11-12

Start with what a detector hears when a chirp passes a mass on two sides. Then derive the arrival time across the lens plane, the exact point-lens amplification and the test a search uses to tell a lensed chirp from an ordinary one. A reproducible tutorial and a paper guide close the course.

1. L1 · Concept

   ## [What a detector hears when one chirp takes two paths](https://sandboxphysics.com/stories/gravitational-wave-lensing/one-chirp-two-paths/)

   A mass near the line of sight splits a gravitational-wave chirp into two delayed copies whose sum swells and fades across frequency.

2. L1 · Chapter

   ## [Why a lens delays a gravitational wave](https://sandboxphysics.com/stories/gravitational-wave-lensing/diffraction-and-the-lens-time-delay/)

   Build the arrival-time surface of a point-mass lens, find its two images and their delay, and see when a wavelength is too long to split.

3. L2 · Chapter

   ## [The exact amplification factor of a point-mass lens](https://sandboxphysics.com/stories/gravitational-wave-lensing/point-lens-amplification-factor/)

   Derive the diffraction integral for a point mass, its closed form, the two-image limit at high frequency and the smooth limit at low frequency.

4. L3 · Chapter

   ## [Can a detector tell a lensed chirp from an ordinary one?](https://sandboxphysics.com/stories/gravitational-wave-lensing/matched-filtering-a-lensed-chirp/)

   Weight two chirps by detector noise, compute their match and estimate how loud a signal must be before a lens shows in the fit.

5. L3 · Method

   ## [Recompute point-lens amplification and test a lens search](https://sandboxphysics.com/stories/gravitational-wave-lensing/recompute-the-point-lens-amplification/)

   Check the closed-form amplification with an independent Fresnel integral, then inject lensed and unlensed chirps into synthetic noise.

6. L4 · Paper guide

   ## [How to read the O3 search for lensed gravitational waves](https://sandboxphysics.com/stories/gravitational-wave-lensing/reading-the-o3-microlensing-search/)

   Read the LIGO-Virgo-KAGRA O3 lensing search for microlensing beats, image pairs and noise that imitates a lens, figure by figure.