INDEX

Preface.

• How a life’s journey leads to writing a book.
• Man as an artist does not play his instrument as a violinist plays his violin, but he spends a lifetime inside his instrument.
• Special thanks 

Introduction. 

• Paradoxa and smart facts in human vision.
• The eye is more than and different to a camera…
• Photoreceptors for CCD cameras and for the eyes.
• The unity of visual objects and the diffraction of their images in seeing.
• Diffraction and interference of light in human vision? With the interference term intelligence comes into the game.
• Interference optics is at home in the micro and in the nano world.
• Light as a particle in the double slit experiment.
• Light as a wave in the double slit experiment.
• Would interference optics be able to explain the non-additivity of luminances in binocular vision?
• Color constancy in daylight vision: the individual and the whole.
• Two axes and a double ‘blind spot’ in each eye are present in the central area of vision.
• The inverted retina construction.
• The unusual position of the peaks of the spectral RGB sensitivity curves in additive tri-chromatic color vision.
• The axis-centered symmetry operations in the central nervous system and in the ocular system.
• From the body’s own reference system to the object-centered 3D coordinates of seen objects.
• Axis-centered ‘global optical column’ in the imaging of visual objects.
• Axis-centered symmetry operations in the central visual pathway.

I. The prenatal development of the eyes and the central visual pathway.

• The development of the visual organ before birth.
• The brain develops the pair of eyes and imposes structural requirements; the eyes develop the central visual pathway to the brain.
• The cellular elements are the cortical micro construction materials for the eye.
• The emergence of the eyes from the forebrain.
• The first setting of the course to the disadvantage of the construction of an ommatidium eye.
• The invagination of the eye cavity: Setting the course for the optical imaging of the visible world.
• The second setting of the course to the disadvantage of a camera construction plan.
• The third setting of the course for an ‘inverted retina’ in favor of a diffractive-optical correlator in the eye.
• The eye axis is the primary axis centering the eye, the visual axis is the secondary axis. The papilla is the primary pole; the fovea is the secondary pole in the retina.
• The development of cellular layers in the cornea and lens of the eye into optical gratings and space gratings.
• The differentiation of the nuclear retinal layers.
• The central cell body accumulation and the shift of the frequency peak of the retinal cell bodies from the papilla to the fovea.
• The splitting of the first distribution peak of the cell bodies and the re-centering of the cell body distribution from the eye axis to the visual axis.
• The development of photoreceptors (cones and rods).
• The development of the photoreceptor outer segments.
• The special position of the foveola funnel in the center of the fovea.
• The distribution patterns of the cones and rods in the retina.
• The sampling geometry of the optic nerve in the bipolar and biaxially centered retina.
• The pre-natal development of the central visual pathway and the cortical requirements for fixating vision. 

II. Diffraction and Interference of light; Information in diffraction patterns.

• Information in the Fraunhofer far-field at diffraction of light on a single aperture.
• Information in the Fraunhofer far-field at diffraction of light on a planar grating.
• Information in the Fraunhofer far-field at diffraction of white (x-ray and visible) light on space-gratings.
• Information in the Fraunhofer far-field at diffraction of light on gratings, which are composed of periodically structured sub-areas.
• Information in the Fraunhofer far-field at optical imaging of a periodic object on to a diffractive space-grating.
• Information in Fourier-space of the imaging lens optics.
• Information in the Fresnel near- or middle-field at diffraction of light on one or multiple apertures.
• Fresnel-Interferences in Talbot-/Fresnel- and fractional Talbot-/Fresnel-planes of diffraction gratings.
• The transition from Fresnel to Fraunhofer diffraction patterns at apertures and gratings.
• The optical imaging of an object on to a hexagonal diffraction grating and the information about object and grating in the fractional Fresnel diffraction patterns.
• The diffraction of light on a ‘hierarchical’ hexagonal grating in the fractional Talbot-/Fresnel-planes.
• How do the inverted retina in the eye and the brain profit by the interference-optical laws.

III. Spatial frequency filtering in the grating-optical correlator of the eye.

• Contrast sensitivity and spatial frequency filtering in the eye.
• The saccades in fixating vision.
• The grating-optical correlator-product made up of object and sensor structures.
• Object structures and object characteristics in the visible.
• The inherent structure of the grating-optical correlator in the eye.
• The grating-optical explanation of the visus-values in daylight and in twilight vision. 

IV. The monocular 3D-depth map in the eye.

• Geometrical optics searching for the monocular 3D-depth map.
• Diffractive optics searching for the monocular 3D-depth map.
• The distances between images of objects in imaging optics and their miniaturization by the Fresnel-interference optics.
o The depth-map of imaging optics.
o The ‘optical swing’ in the eye: object fixation and accommodation of the imaging optics to the object distance.
o Gratings in image space compress the optical 3D-depth map.
o A constant photoreceptor matrix at the central image plane of the fixated object.
• Diffractive optics and the Fresnel ‘phase-retrieval’ depth map.
• Information about the (hierarchical) grating and about local objects in the 3D-depth map.
• The miniaturized monocular 3D-depth map in the eye and the three typical marginalities of accommodation in the ‘optical swing’.
• Does the cortical visual center V1 dispose of a monocular 3D-depth map?

V. Spectral space-grating optics in the diffractive-optical correlator of the human eye.

• Well-known and less-known facts regarding human color vision.
• Physical equilibrium in the white spectrum and physiological equilibrium in the RGB-white-sensation of color vision.
• Diffraction and interference of light on the planar grating and on the 3D-space-grating; Fresnel medium-field and Fraunhofer far-field interferences.
• The dealing of the sensory organs with the reciprocity of wavelength λ and frequency ν in νλ = 1.
• Interferences in the Fresnel near- or medium-field at diffraction of light on a space- grating located in image space of an optical imaging system.
• The mathematical equations for the diffractive interference-optical light double cone transformations in space-gratings.
• The application of the von-Laue equation to hexagonal space-gratings.
• The chromatic tuning of a space-grating.
• The crystal-optical resonance factor.
• The harmonically linked RGB-diffraction order triplet.
• The Fresnel-interference optics for light double cones with different apertures.
• The longer and shorter wavelengths in comparison to =559nm in the 111R-diffraction order.
• Wavelengths contributing by means of the same light cone to all three RGB-sensitivity curves.
• Space-grating optics provides the complete RGB sensitivity curves.
• The modulation of the spectral maxima along the outer segments of the cones in reciprocal space.
• The significance of the interference terms for the light-like geometry in space-grating optics.
• The chromatic harmonics in vision and in hearing.
• The description of the double cone transformations of the Fresnel-interferences in the space-grating by means of the so-called reciprocal von-Laue equation.
• The spectral space-grating optics and the monocular 3D-depth map.
• The importance of the spectral space-grating optics for the better understanding of human color vision. 

VI. Space-gratings in aperture and image space of optics: new insights into RGB-based achromatic and color vision, opponent colors, color constancy, Purkinje-shift and Bezold-Brücke phenomenon. 

• Space-gratings in aperture and image space of the eye, their contribution to RGB color vision.
• White and Gray achromatic sensations are equilibria of local and global RGB-data.
• Color sensations are disequilibria of local and global RGB-data.
o The BLUE-TURQUOISE sensation.
o The GREEN sensation.
o The YELLOW sensation.
o The RED sensation.
• Color constancy in the change between white and colored illuminations.
• The relation-building between local and global RGB-data in the grating-optical correlator.
• The complete hardware of the grating-optical correlator in the eye.
• Space-gratings in aperture and image space of the eye and their contribution to the ‘paradoxical’ colored shadows in twilight.
• The repartition of the light onto two lights in twilights.
• Colored lights in twilights and their ‘normal’ colored shadows.
• Goethe‘s experiment with the full moon and a candle.
• The world of fairies in Goethe‘s walking tour in the Harz mountains.
• The ‘normal’ colored shadows in the closed opponent color wheel.
• The ‘paradoxical’ colored shadows in twilights.
• The opponent color after-images in color vision.
• Space-grating optics and scotopic vision: the intensity-adaptive Purkinje-shift.
• The Bezold-Brücke phenomenon in human color vision.

VII. The grating-optical layered pre-processing of the visible in global and local optical columns. 

• The pre-processing of the visible in ‘global’ optical columns.
• The pre-processing of the visible in ‘local’ optical columns.
• The layered grating-optical and neuronal information pre-processing in the ‘inverted’ retina.
• The specific visual functionalities in the layered grating-optical information pre-processing.

VIII. Object classification and object identification in vision. 

• How vision ascribes a meaning to things.
• The polarity of classification and identification.
• The correlator-optical hardware of the eyes and their visual pathway available for object classification and identification.
• At object classification and identification, vision reduces all objects to relations.
• The polarly centered processing of the shape of right triangles in the hexagonal net and the determination of their similarity.
• The polarly centered processing of the shape of quadrangles in the hexagonal net and the determination of their similarity.
• The (log-) polar ascertainment of a typically human figure.
• Harmonics-analyses and saccades in vision.
• The acoustic melody as an invariant in human hearing.
• From the (log-) polar shape analysis to the melody of a visible object: the harmonic Pythagoras’ theorem analysis of the visible.
• The differentiation between object-categories in hearing and in vision.
• Object identification succeeds best in fixating vision, object classification in non-fixating vision.
• The correlate of the visible in the eye.

IX. Summary.

X. Epilogue.

• How the visible world gets into the head…
• What in human vision holds the world together in its innermost…
• What in the bio-engineering of a retina implant of the next generations is technically due…
• What the grating-optical correlator and diffractive interference optics in the eye contribute to our experiencing reality…
• The path of learning in vision, of understanding and naming of objects is long…

Bibliography. 

Appendix: Prevention of MYOPIA: the eye ought to exercise the use oft he 3rd dimension of the visible at an early age.