## 5 Methods for Angular Dispersion Detection
### Two-Dimensional Detection Method for Propagation Direction Angular Dispersion  
When a broadband light beam is affected by angular dispersion, its spectral components will propagate in various directions. If the beam is focused directly on the sensor chip of a two-dimensional detector by an achromatic imaging element, a relatively elongated spot will appear in the image compared to a beam without the effect of dispersion. The intensity distribution of this elongated spot is in direct correlation with the spectral angular deviation. However, the spot itself is not suitable for accurate measurements. On one hand, chromatic aberration of the spot must be separated from optical aberrations of different nature. On the other hand, this elongated spot contains no information on the spectral calibration required for the measurement, _i.e._, different parts of the spot cannot be matched with the frequency of the corresponding spectral components. Both problems can be eliminated with the purposive spectral modulation and calibration of the broadband beam. A method for single-shot, two-dimensional measurement of propagation direction angular dispersion of broadband light sources (e.g., ultrashort laser beams) was introduced recently. In this case, spectral calibration is achieved by spectrally filtering the beam in order to create well-separated peaks in the spectrum. Since these components are still overlapping spatially, we use an achromatic lens to image them onto a two-dimensional detector. In this way, the spectrally separated components of an angularly dispersed beam will appear as dissociated spots on the surface of the detector according to the orientation of the angular dispersion. The role of the spectral filter can be filled with various, either passive or active solutions. For example, multiple bandpass interference filters or wavelength-selective reflectors can be used for this purpose. Another very simple idea is to block parts of the spectrally resolved beam in the stretcher; although it might be not suitable, if the stretcher itself is the object of examination. Acousto-optical programmable modulators can be used also to create an arbitrarily modified spectrum. A less expensive solution to create separated spectral peaks is the use of a Fabry-Perot interferometer (_FPI_) [104] with either adjustable or fixed baselength, which allows high spectral purity when one is using high-reflection mirrors. When it is equipped with a precision translator, the wavelength spacing of the transmitted spectrum can be controlled easily through its baselength. This feature makes the _FPI_ the optimal choice as the spectral filtering device. The scheme of the technique can be seen in Figure 14a, where a _FPI_ is pictured as a spectral filter. A broadband beam with unknown angular dispersion is propagating through the partially reflecting mirrors of the _FPI,_ where the spectrum of the beam becomes modulated, and thus well defined, sharp spectral peaks appear. The transmitted parts of the spectrum preserve their original propagation directions, which--in case of angular dispersion--can be different for each spectral component. However, the spatial distributions of these spectrally separated beams are still overlapping. For this reason, an achromatic lens is positioned after the _FPI_ to image the beams onto the chip of a two-dimensional detector. When the beam has weak angular dispersion only, it is possible that the spectral spots cannot be separated effectively with the base length modulation of the _FPI_. In these cases, a grating or prism with very well-known and calibrated angular dispersion can be inserted between the _FPI_ and the achromatic lens (see Figure 14b). It provides an additional constant bias in the angular dispersion only, but with the spots very well separated, it increases the precision of the extraction of the spot coordinates, and by that, the precision of the measurement.