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Gravitational Lensing


Admission requirements

The student is assumed to have a working knowledge of geometrical optics and gravitational potential theory. Basic familiarity with astronomical objects (stars, galaxies, clusters of galaxies, large-scale structure) is assumed. Some knowledge of cosmology and general relativity is useful, but not essential. In terms of the Leiden curriculum, the astronomy BSc provides a good preparation.


Light rays are deflected by gravitational fields, which makes massive bodies act like lenses. Although the effect is incredibly weak in terrestrial settings, in astronomical and cosmological settings it becomes observable. This course describes the phenomenon quantitatively, and introduces the various ways in which astronomers use it as a tool to interpret observations.

Topics that will be covered include

  • basic principles

    • light deflection by gravitational fields in Newtonian Gravity and General Relativy
    • the lensing equation and sample solutions (including multiple imaging)
    • the Fermat potential and time delays
    • shear, convergence and magnification
    • the mass-sheet degeneracy
  • strong lensing and its applications:

    • the gravitational telescope
    • galaxy and galaxy cluster masses
    • milli-lensing and halo substructure
    • time delay cosmography
  • microlensing and its applications:

    • MACHOs in the haloes of galaxies
    • stellar populations
    • binary lenses and the lensing effect of planets
  • weak lensing and its applications

    • shape noise and measuring weak lensing
    • tangential shear and mass distributions of galaxies and galaxy clusters
    • mass mapping
    • cosmic shear and large-scale structure

Course objectives

Upon completion of this course you will be able to measure and interpret gravitational lensing in astronomical data, in the context of strong, micro- and weak lensing.

Soft skills

This is course is not designed to develop soft skills per se.


See Astronomy master schedules


Brightspace will be used to communicate with students and to share lecture slides, homework assignments, and any extra materials. To have access, you need a student ULCN account.

Reading list

Basics of lensing, Kuijken:

As reference we will use the 33rd Saas-Fee Advanced course on Gravitational lensing.

Strong lensing, C.Kochanek:
Microlensing, J. Wambsganss:
Weak lensing, P. Schneider:


Via uSis. More information about signing up for your classes can be found here. Exchange and Study Abroad students, please see the Prospective students website for information on how to apply.

Contact information


Prof.dr. K.H. Kuijken

Prof.dr. H. Hoekstra

Dr. A. Sonnenfeld

Assistants: Shun Sheng Li, Anna Balaudo