Strehl ratio
Encyclopedia
The Strehl ratio, named after the German physicist and mathematician Karl Strehl (1864-1940), is a measure for the optical quality of telescopes and other imaging instruments. It is defined as the ratio of the observed peak intensity at the detection plane from a point source
as compared to the theoretical maximum peak intensity of a perfect imaging system working at the diffraction limit. This is closely related to the sharpness criteria for optics defined by Karl Strehl. It can be expressed as
with sigma (σ) being the root mean square deviation
of the wavefront
and lambda (λ) being the wavelength
. Unless stated otherwise, the Strehl ratio is usually calculated at the best focus
of the imaging system under study.
in the presence of atmospheric turbulence and assess the performance of any adaptive optical
correction system. It is also used for the selection of short exposure images in the lucky imaging
method.
In industry the Strehl ratio has become a popular way to summarize the performance of an optical design because it gives the performance of a real system, of finite cost and complexity, in terms of a theoretically perfect system which would be infinitely expensive and complex to build and would still have a finite point spread function. It provides a simple method to compare a system with a Strehl ratio of, for example 0.95 is good enough, or whether twice as much should be spent to try to get a Strehl ratio of perhaps 0.97 or 0.98.
Visually, diffraction
of light is imperfect, even in a perfect optical system. This leads to an observable point spreading phenomenon which produces the so-called Airy disk or disk of light when point sources such as distant stars are magnified. The intensity distribution in the image plane
of a point source is generally called the point spread function
. The Strehl ratio compares the differences between theoretically perfect point spread and the actual point spread of a given optical device.
s, but excludes most photographic systems, for example. The Strehl ratio has been linked via the work of Marechal to an aberration tolerancing theory which is very useful to designers of well corrected optical systems, allowing a meaningful link between the aberrations of geometrical optics
and the diffraction theory of physical optics. A significant shortcoming of the Strehl ratio as a method of image assessment is that, although it is relatively easy to calculate for an optical design prescription on paper, it is normally difficult to measure for a real optical system, not least because the theoretical maximum peak intensity is not readily available.
Point source
A point source is a localised, relatively small source of something.Point source may also refer to:*Point source , a localised source of pollution**Point source water pollution, water pollution with a localized source...
as compared to the theoretical maximum peak intensity of a perfect imaging system working at the diffraction limit. This is closely related to the sharpness criteria for optics defined by Karl Strehl. It can be expressed as
with sigma (σ) being the root mean square deviationRoot mean square deviation
The root-mean-square deviation is the measure of the average distance between the atoms of superimposed proteins...
of the wavefront
Wavefront
In physics, a wavefront is the locus of points having the same phase. Since infrared, optical, x-ray and gamma-ray frequencies are so high, the temporal component of electromagnetic waves is usually ignored at these wavelengths, and it is only the phase of the spatial oscillation that is described...
and lambda (λ) being the wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
. Unless stated otherwise, the Strehl ratio is usually calculated at the best focus
Focus (optics)
In geometrical optics, a focus, also called an image point, is the point where light rays originating from a point on the object converge. Although the focus is conceptually a point, physically the focus has a spatial extent, called the blur circle. This non-ideal focusing may be caused by...
of the imaging system under study.
Usage
The ratio is commonly used to assess the quality of astronomical seeingAstronomical seeing
Astronomical seeing refers to the blurring and twinkling of astronomical objects such as stars caused by turbulent mixing in the Earth's atmosphere varying the optical refractive index...
in the presence of atmospheric turbulence and assess the performance of any adaptive optical
Adaptive optics
Adaptive optics is a technology used to improve the performance of optical systems by reducing the effect of wavefront distortions. It is used in astronomical telescopes and laser communication systems to remove the effects of atmospheric distortion, and in retinal imaging systems to reduce the...
correction system. It is also used for the selection of short exposure images in the lucky imaging
Lucky imaging
Lucky imaging is one form of speckle imaging used for astronomical photography. Speckle imaging techniques use a high-speed camera with exposure times short enough so that the changes in the Earth's atmosphere during the exposure are minimal.With lucky imaging, those optimum exposures least...
method.
In industry the Strehl ratio has become a popular way to summarize the performance of an optical design because it gives the performance of a real system, of finite cost and complexity, in terms of a theoretically perfect system which would be infinitely expensive and complex to build and would still have a finite point spread function. It provides a simple method to compare a system with a Strehl ratio of, for example 0.95 is good enough, or whether twice as much should be spent to try to get a Strehl ratio of perhaps 0.97 or 0.98.
Further explanation
Diffraction
Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...
of light is imperfect, even in a perfect optical system. This leads to an observable point spreading phenomenon which produces the so-called Airy disk or disk of light when point sources such as distant stars are magnified. The intensity distribution in the image plane
Image plane
In 3D computer graphics, the image plane is that plane in the world which is identified with the plane of the monitor. If one makes the analogy of taking a photograph to rendering a 3D image, the surface of the film is the image plane. In this case, the viewing transformation is a projection that...
of a point source is generally called the point spread function
Point spread function
The point spread function describes the response of an imaging system to a point source or point object. A more general term for the PSF is a system's impulse response, the PSF being the impulse response of a focused optical system. The PSF in many contexts can be thought of as the extended blob...
. The Strehl ratio compares the differences between theoretically perfect point spread and the actual point spread of a given optical device.
Limitations
Characterizing the form of the point-spread function by a single number, as the Strehl Ratio does, will only be meaningful and sensible if the point-spread function is little distorted from its ideal (aberration-free) form. This is valid for well corrected systems that operate close to the diffraction limit. This includes most telescopes and microscopeMicroscope
A microscope is an instrument used to see objects that are too small for the naked eye. The science of investigating small objects using such an instrument is called microscopy...
s, but excludes most photographic systems, for example. The Strehl ratio has been linked via the work of Marechal to an aberration tolerancing theory which is very useful to designers of well corrected optical systems, allowing a meaningful link between the aberrations of geometrical optics
Geometrical optics
Geometrical optics, or ray optics, describes light propagation in terms of "rays". The "ray" in geometric optics is an abstraction, or "instrument", which can be used to approximately model how light will propagate. Light rays are defined to propagate in a rectilinear path as far as they travel in...
and the diffraction theory of physical optics. A significant shortcoming of the Strehl ratio as a method of image assessment is that, although it is relatively easy to calculate for an optical design prescription on paper, it is normally difficult to measure for a real optical system, not least because the theoretical maximum peak intensity is not readily available.