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  • When the image of an object, made by an optical system (e.g. by a microscope or a telescopes), must be observed by a human eye or sent to another optical system, the rays travelling from the edges of the object to the edges of the image, can span a so large angles that they cannot be collected by the eyepiece or by the successive optics. The situation is sketched in the following figures.


    Fig. 11-Microscopy sketch



    Fig.12- Telescopes sketch

    It is obvious that the second lens (e.g. an eyepiece for direct observation or another optical system) will collect only a portion of the incoming rays: consequently the radiation coming from the object edges will be partially or totally lost and the image would result attenuated at its edges (vignetting).

    In order to avoid such an effect and eliminate the losses from all the points of the image a "field lens" can be used. Its way of working is shown in the following pictures:


    Fig.13 – Microscopy with a field lens



    Fig.14 – Telescopes with a field lens

    The field lens, placed directly or close to the image made by the objective, forms an image of the objective exit pupil on the eyepiece, or on the entrance pupil of the optical system following the first instrument. Since the field lens produces only a deviation of the principal rays, without change the relative position of their associated rays, it does not introduce any aberration in the correct formation of the image. However it should be noticed that in order to decrease the beam size impinging on the final lens (the eyepiece), it was necessary to rotate the principal rays and the corresponding associated rays. The principal rays connect each point of the object to the centre of the optics entrance pupil. The associated rays are all the rays that connect the same point on the real object to all the points of the entrance pupil.

    This means that the angular amplitude of the beams coming from each point of the real object remains unchanged. Hence the field lens works in such way that each point of the object is viewed with the same angular amplitude: if the eyepiece, or the optical system following the instrument, has a smaller diameter than the beam section, the field lens homogenize the losses for each point of the field view, but it cannot remove the total losses. Given the size of the image and of the eyepiece entrance pupil, the field lens must form the image of the exit pupil of the instrument objective on the entrance pupil of the eyepiece. If the image size of the objective is smaller or equal to the size of the entrance pupil of the eyepiece, the eyepiece is able to receive all the objective crossing energy.

    The field lens must be calculated and placed in order to obtain the magnification required.

    To do this the following formula can be applied:

    where p is the distance between the objective and the field lens, q is the distance between field lens and the eyepiece and f is the lens focal length.

    Fig. 15 – Size and position of a field lens.

    Since the field lens is placed on the image (or close to it), it is viewed, through the eyepiece, as coincident with the image itself. Hence it has to be devoid by any defects (scratches and dust), but it can be used with a grating, eventually graduated,or with a crosshair engraved on it.

    Often the field lens is inserted into the eyepiece (it is the first lens from the objective).

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