Abbe theory considers the image formation process in an optical system (OS) in two stages: obtaining a spatial spectrum in a back focal plane and composing an output magnified image in an image plane. Abbe-Porter experiments are bright illustrations of this theory. This theory can be extended from two-dimensional (2D) case to three-dimensional (3D) one. It has to consider the grating inclined relatively the optical axis round the axis parallel to the grating slits. It makes possible calculations of the minimum resolvable period (MRP) of an OS as the functions of the angle of grating inclination. The paper presents the optical setup for observation of spatial spectrums and magnified images in case of the inclined gratings. It has been demonstrated that this spatial spectrum is in full compliance with the proposed theory. It has been also shown that the MRP exists in case of inclined gratings in full compliance with the theory. This experiment may be considered as one of the very interesting experiments for demonstration, understanding and explanation of the physical process of 3D image formation by an OS. Famous Abbe experiment becomes only the partial case and, of course, the most important case of this experiment with an inclined grating.
The interesting experiments for investigation of image formation in optical microscopes have been done by E. Abbe, A. Porter and L. Mandelshtam. These experiments have become the classical ones and they are widely used for explanation of Fourier optics. The principal disadvantage of them is difference in optical schemes for observation of object images and their spatial spectrums. The proposed optical setup makes possible demonstration of two stages of image formation – obtaining a spatial spectrum and composing a magnified object image – together in one plane. This setup contains two imaging channels separated by a beam splitter after a microscope objective. The first one forms a magnified object image, the second one – an image of a spatial spectrum. These images may be observed on a screen, via eyepieces or using image sensors. Any occluding of spectrum zones becomes visible and it leads to the corresponded changes in an object image. This optical setup would be useful for optical education and research.
The paper presents the new approach that includes technique, scheme and instruments for precise calibration of space-borne and airborne visible infrared imaging radiometers (VIIRs). The key component of this technique is the precise uniform light source based on optically-interconnected integrating spheres. The light source contains several (5…11) primary integrating spheres of small diameters which are installed on a secondary integrating sphere of bigger diameter. The initial light sources – halogen lamps or light emitted diodes are installed inside the primary integrating spheres. These spheres are mounted on the secondary integrating sphere. The radiation comes from the primary integrating spheres to the secondary one through diaphragms which diameters can be varied. The secondary integrating sphere has an output aperture where uniform radiance emits. As a result the output radiance can be varied in extremely wide range – up to 800 W/(st·m2) with dynamic range 1 000 000 – without any change of spectral characteristics. Non-uniformity of the radiance distribution throughout the output aperture can be smaller 0.5 % because the secondary integrating sphere is illuminated uniformly and it does not contain lamps inside. The paper discusses the requirements to calibration system, the application of this light source in calibration procedures, metrological aspects of radiometric calibration.