What is a 4F optical system?

Introduction. The 4f system is a commonly used optical relay that usually consists of two positive lenses with the input plane located one focal length (f1) in front of Lens 1 and the output plane located one focal length (f2) after Lens 2. The magnification is found to be equal to −f2∕f1.

What does a 4F system do?

4F system (as Mark pointed out) allows accessing the Fourier plane. By placing a “spatial frequency filter” 1f in-front of the first lens and another one 1f behind the first lens, a combined effect is produced 1f behind the second lens.

How do you align a 4F system?

A 4F system will be set up with three lenses, each lens having an EFL of 100mm. At the same time, an alignment telescope equipped with a CCD camera will be used to align the 4F system. That means to place all the optical centers of curvature (C of C) of all the surfaces on the system optical axis.

What is the Fourier plane?

Fourier optics is the study of classical optics using Fourier transforms (FTs), in which the waveform being considered is regarded as made up of a combination, or superposition, of plane waves. In this case, a Fraunhofer diffraction pattern is created, which emanates from a single spherical wave phase center.

What is 4f correlator?

The 4f correlator is in essence an optical relay that usually consists of two lenses. The input plane is one focal length in front of Lens 1 while the output plane is located one focal length after Lens 2. A 1:1 relay (−1 magnification) and can be achieved if the two lenses have the same focal length.

What is coherent transfer function?

The transfer function itself is merely the scaled version of pupil function for coherent light, and pupil autocorrelation for incoherent light. In effect, the system impulse response acts as a smoothing spatial filter, softening edges, reducing amplitude, and suppressing high frequency distributions.

Why is a lens a Fourier transform?

Strictly speaking the far-field diffraction pattern can only be observed at infinity. By placing a lens after the diffracting aperture the plane at infinity is imaged onto the focal plane of the lens. This explains why a lens can perform a Fourier transform.

Why a lens is a Fourier transform?

By placing a lens after the diffracting aperture the plane at infinity is imaged onto the focal plane of the lens. This explains why a lens can perform a Fourier transform. and v are normalized coordinates in the transform plane. The object (a transparency) is illuminated by a coherent plane wave.

What is the fundamental idea of Fourier optics?

Based on diffraction theory and the propagation of the light, Fourier optics is a powerful tool allowing the estimation of a visible-range imaging system to transfer the spatial frequency components of an object. The analyses of the imaging systems can thus be performed and the the performance retrieved.

What is modulation transfer function of the optical system?

The modulation transfer function is the magnitude response of the optical system to sinusoids of different spatial frequencies. When we analyze an optical system in the frequency domain, we consider the imaging of sinewave inputs (Fig. 1.8) rather than point objects.

What is point spread function in image processing?

The ideal point spread function (PSF) is the three-dimensional diffraction pattern of light emitted from an infinitely small point source in the specimen and transmitted to the image plane through a high numerical aperture (NA) objective.

How are 4F systems used in real life?

By passing your real-life system through a 4f system, the Fourier transformation of your image will interact with your target-mask at the Fourier plane and create a specific response where there is a match. We most recently used a 4F system in a custom eye aberrometer. An eye aberrometer measures the wavefront of light as it goes through the eye.

How does Fourier transformation work in a 4F system?

It can be a flow of liquids where you want to detect your bacteria, the satellite image on enemy territory, or a user scanning an access card. By passing your real-life system through a 4f system, the Fourier transformation of your image will interact with your target-mask at the Fourier plane and create a specific response where there is a match.

How big is the pupil Mask of a 4F lens?

illuminated by an on-axis plane wave at wavelength λ=0.5µm. The 4F system consists of two identical lenses of focal length f=20cm. A pupil mask of diameter (aperture) 3cm is placed at the Fourier plane, symmetrically about the optical axis.

What is the structure of a 4F correlator?

Basic structure of a 4f optical system. The 4f correlator is in essence an optical relay that usually consists of two lenses. The input plane is one focal length in front of Lens 1 while the output plane is located one focal length after Lens 2.

What is a 4F optical system? Introduction. The 4f system is a commonly used optical relay that usually consists of two positive lenses with the input plane located one focal length (f1) in front of Lens 1 and the output plane located one focal length (f2) after Lens 2. The magnification is found to be…