El problema de Alhacén

El presente documento es un estudio detallado del problema conocido bajo el título de Problema de Alhacén. Este problema fue formulado en el siglo X por el filósofo y matemático árabe conocido en occidente bajo el nombre de Alhacén. El documento hace una breve presentación del filósofo y una breve reseña de su trascendental tratado de óptica Kitab al-Manazir. A continuación el documento se detiene a estudiar cuidadosamente los lemas requeridos para enfrentar el problema y se presentan las soluciones para el caso de los espejos esféricos (convexos y cóncavos), cilíndricos y cónicos. También se ofrece una conjetura que habría de explicar la lógica del descubrimiento implícita en la solución que ofreció Alhacén. Tanto los lemas como las soluciones se han modelado en los software de geometría dinámica Cabri II-Plus y Cabri 3-D. El lector interesado en seguir dichas modelaciones debe contar con los programas mencionados para adelantar la lectura de los archivos. En general, estas presentaciones constan de tres partes: (i) formulación del problema (se formula en forma concisa el problema); (ii) esquema general de la construcción (se presentan los pasos esenciales que conducen a la construcción solicitada y las construcciones auxiliares que demanda el problema), esta parte se puede seguir en los archivos de Cabri; y (iii) demostración (se ofrece la justificación detallada de la construcción requerida). Los archivos en Cabri II plus cuentan con botones numerados que pueden activarse haciendo “Click” sobre ellos. La numeración corresponde a la numeración presente en el documento. El lector puede desplazar a su antojo los puntos libres que pueden reconocerse porque ellos se distinguen con la siguiente marca (º). Los puntos restantes no pueden modificarse pues son el resultado de construcciones adelantadas y ajustadas a los protocolos recomendados en el esquema general.

Cavity-enhanced absorption: detection of nitrogen dioxide and iodine monoxide using a violet laser diode

We present an application of cavity-enhanced absorption spectroscopy with an off-axis alignment of the cavity formed by two spherical mirrors and with time integration of the cavity-output intensity for detection of nitrogen dioxide (NO2) and iodine monoxide (IO) radicals using a violet laser diode at lambda = 404.278 nm. A noise-equivalent (1sigma = root-mean-square variation of the signal) fractional absorption for one optical pass of 4.5x10(-8) was demonstrated with a mirror reflectivity of similar to0.99925, a cavity length of 0.22 m and a lock-in-amplifier time constant of 3 s. Noise-equivalent detection sensitivities towards nitrogen dioxide of 1.8x10(10) molecule cm(-3) and towards the IO radical of 3.3x10(9) molecule cm(-3) were achieved in flow tubes with an inner diameter of 4 cm for a lock-in-amplifier time constant of 3 s. Alkyl peroxy radicals were detected using chemical titration with excess nitric oxide (RO2 + NO --> RO + NO2). Measurement of oxygen-atom concentrations was accomplished by determining the depletion of NO2 in the reaction NO2 + O --> NO + O-2. Noise-equivalent concentrations of alkyl peroxy radicals and oxygen atoms were 3x10(10) molecule cm(-3) in the discharge-flow-tube experiments.

Construção de um interferômetro de Bath para análise do comportamento da superfície de vidros usados na confecção de espelhos côncavos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Geometrical attenuation factors for gamma radiation from cylindrical and spherical surface sources /

Issued September 15, 1963.

Limits of spherical blur determined with an adaptive optics mirror

We extended an earlier study (Vision Research, 45, 1967–1974, 2005) in which we investigated limits at which induced blur of letter targets becomes noticeable, troublesome and objectionable. Here we used a deformable adaptive optics mirror to vary spherical defocus for conditions of a white background with correction of astigmatism; a white background with reduction of all aberrations other than defocus; and a monochromatic background with reduction of all aberrations other than defocus. We used seven cyclopleged subjects, lines of three high-contrast letters as targets, 3–6 mm artificial pupils, and 0.1–0.6 logMAR letter sizes. Subjects used a method of adjustment to control the defocus component of the mirror to set the 'just noticeable', 'just troublesome' and 'just objectionable' defocus levels. For the white-no adaptive optics condition combined with 0.1 logMAR letter size, mean 'noticeable' blur limits were ±0.30, ±0.24 and ±0.23 D at 3, 4 and 6 mm pupils, respectively. White-adaptive optics and monochromatic-adaptive optics conditions reduced blur limits by 8% and 20%, respectively. Increasing pupil size from 3–6 mm decreased blur limits by 29%, and increasing letter size increased blur limits by 79%. Ratios of troublesome to noticeable, and of objectionable to noticeable, blur limits were 1.9 and 2.7 times, respectively. The study shows that the deformable mirror can be used to vary defocus in vision experiments. Overall, the results of noticeable, troublesome and objectionable blur agreed well with those of the previous study. Attempting to reduce higher-order aberrations or chromatic aberrations, reduced blur limits to only a small extent.

Modeling videokeratoscopic height data with spherical harmonics

Purpose: All currently considered parametric models used for decomposing videokeratoscopy height data are viewercentered and hence describe what the operator sees rather than what the surface is. The purpose of this study was to ascertain the applicability of an object-centered representation to modeling of corneal surfaces. Methods: A three-dimensional surface decomposition into a series of spherical harmonics is considered and compared with the traditional Zernike polynomial expansion for a range of videokeratoscopic height data. Results: Spherical harmonic decomposition led to significantly better fits to corneal surfaces (in terms of the root mean square error values) than the corresponding Zernike polynomial expansions with the same number of coefficients, for all considered corneal surfaces, corneal diameters, and model orders. Conclusions: Spherical harmonic decomposition is a viable alternative to Zernike polynomial decomposition. It achieves better fits to videokeratoscopic height data and has the advantage of an object-centered representation that could be particularly suited to the analysis of multiple corneal measurements.

Influence of spherical intraocular lens implantation and conventional laser in situ keratomileusis on peripheral ocular aberrations

Aim: To measure the influence of spherical intraocular lens implantation and conventional myopic laser in situ keratomileusis on peripheral ocular aberrations. Setting: Visual & Ophthalmic Optics Laboratory, School of Optometry & Institute of Health and Biomedical Innovation, Queensland University of Technology, Brisbane, Australia. Methods: Peripheral aberrations were measured using a modified commercial Hartmann-Shack aberrometer across 42° x 32° of the central visual field in 6 subjects after spherical intraocular lens (IOL) implantation and in 6 subjects after conventional laser in situ keratomileusis (LASIK) for myopia. The results were compared with those of age matched emmetropic and myopic control groups. Results: The IOL group showed a greater rate of quadratic change of spherical equivalent refraction across the visual field, higher spherical aberration, and greater rates of change of higher-order root-mean-square aberrations and total root-mean-square aberrations across the visual field than its emmetropic control group. However, coma trends were similar for the two groups. The LASIK group had a greater rate of quadratic change of spherical equivalent refraction across the visual field, higher spherical aberration, the opposite trend in coma across the field, and greater higher-order root-mean-square aberrations and total root-mean-square aberrations than its myopic control group. Conclusion: Spherical IOL implantation and conventional myopia LASIK increase ocular peripheral aberrations. They cause considerable increase in spherical aberration across the visual field. LASIK reverses the sign of the rate of change in coma across the field relative to that of the other groups. Keywords: refractive surgery, LASIK, IOL implantation, aberrations, peripheral aberrations

Spherical image-based visual servo and structure estimation

This paper presents a formulation of image-based visual servoing (IBVS) for a spherical camera where coordinates are parameterized in terms of colatitude and longitude: IBVSSph. The image Jacobian is derived and simulation results are presented for canonical rotational, translational as well as general motion. Problems with large rotations that affect the planar perspective form of IBVS are not present on the sphere, whereas the desirable robustness properties of IBVS are shown to be retained. We also describe a structure from motion (SfM) system based on camera-centric spherical coordinates and show how a recursive estimator can be used to recover structure. The spherical formulations for IBVS and SfM are particularly suitable for platforms, such as aerial and underwater robots, that move in SE(3).

A practical implementation of a continuous isotropic spherical omnidirectional drive

This paper presents a continuous isotropic spherical omnidirectional drive mechanism that is efficient in its mechanical simplicity and use of volume. Spherical omnidirectional mechanisms allow isotropic motion, although many are limited from achieving true isotropic motion by practical mechanical design considerations. The mechanism presented in this paper uses a single motor to drive a point on the great circle of the sphere parallel to the ground plane, and does not require a gearbox. Three mechanisms located 120 degrees apart provide a stable drive platform for a mobile robot. Results show the omnidirectional ability of the robot and demonstrate the performance of the spherical mechanism compared to a popular commercial omnidirectional wheel over edges of varying heights and gaps of varying widths.

Mechanism of Resistance to Rice Tungro Spherical Virus (RTSV)

RTSV is one of two viruses that cause tungro disease. RTSV is independently transmitted, whereas the other virus, rice tungro bacilliform virus (RTBV), is dependent on RTSV for its transmission by the green leafhopper (GLH), Nephotettix virescens. The occurrence and spread of tungro disease therefore depend on the presence of RTSV in the field. Resistance to RTSV infection would slow down the spread of the disease.

Differentiation of Rice Tungro Spherical Virus Variants by RTPCR and RFLP

Differentiation of rice tungro spherical virus variants by RTPCR and RFLP tungro bacilliform virus (RTBV), the other causal agent, which causes the symptoms. RTSV is a single-stranded RNA virus of 12,180 nucleotides (Hull 1996).

Complete Nucleotide Sequence of Rice Tungro Spherical Virus Genome of a Highly Virulent Strain Vt6

The complete nucleotide sequence of rice tungro spherical virus (RTSV) strain Vt6, originally from Mindanao, the Philippines, with higher virulence to resistant rice cultivars, was determined and compared with the published sequence for the Philippine-type strain A (RTSV-A-Shen). It was reported that RTSV-A was not able to infect a rice resistant cultivar TKM 6 (10). RTSV-Vt6 and RTSV-A-Shen share 90% and 95% homology at nucleotide and amino-acid levels, respectively. The N-terminal leader sequence of RTSV-Vt6 contained a 39-amino acids-region (positions 65 to 103) which was totally different from that of RTSV-A-Shen; the difference resulted from frame shifting by nucleotide insertions and deletions. To confirm the amino-acid sequence differences of the leader polypeptide, the same region was cloned and sequenced using a newly obtained variant of RTSV-type 6, which had been collected in the field of IRRI, and seven field isolates from Mindanao, the Philippines. Since all the sequences of the target region are identical to that of the Vt6 leader polypeptide, the sequence difference in the leader region seems not to correlate with the virulence of Vt6.

Genetic Diversity of Rice Tungro Spherical Virus in Tungro-Endemic Provinces of the Philippines and Indonesia

The two adjacent genes of coat protein 1 and 2 of rice tungro spherical virus (RTSV) were amplified from total RNA extracts of serologically indistinguishable field isolates from the Philippines and Indonesia, using reverse transcriptase polymerase chain reaction (RT-PCR). Digestion with HindIII and BstYI restriction endonucleases differentiated the amplified DNA products into eight distinct coat protein genotypes. These genotypes were then used as indicators of virus diversity in the field. Inter- and intra-site diversities were determined over three cropping seasons. At each of the sites surveyed, one or two main genotypes prevailed together with other related minor or mixed genotypes that did not replace the main genotype over the sampling time. The cluster of genotypes found at the Philippines sites was significantly different from the one at the Indonesia sites, suggesting geographic isolation for virus populations. Phylogenetic studies based on the nucleotide sequences of 38 selected isolates confirm the spatial distribution of RTSV virus populations but show that gene flow may occur between populations. Under the present conditions, rice varieties do not seem to exert selective pressure on the virus populations. Based on the selective constraints in the coat protein amino acid sequences and the virus genetic composition per site, a negative selection model followed by random-sampling events due to vector transmissions is proposed to explain the inter-site diversity observed

Inheritance of Resistance to Rice Tungro Spherical Virus in a Near-Isogenic Line Derived from Utri Merah and in Rice Cultivar TKM6

Resistance to rice virus diseases is an important requirement in many Southeast Asian rice breeding programs. Inheritance of resistance to rice tungro spherical virus (RTSV) in TW5, a near-isogenic line derived from Indonesian rice cultivar Utri Merah, was compared to that in TKM6, an Indian rice cultivar. Both TKM6 and Utri Merah are cultivars resistant to RTSV infections. Crosses were made between TKM6 and TN1, a susceptible cultivar, and between TW5 and TN1, and F3 lines were evaluated for their resistance to RTSV using two RTSV inoculum sources and a serological assay (ELISA). In TKM6, the resistance to the mixture of RTSV-V + RTBV inoculum source was controlled by a single recessive gene, whereas in TW5, the resistance was controlled by two recessive genes. A single recessive gene, however, controlled the resistance in TW5 when another RTSV variant, RTSV-VI, was used, suggesting that the resistance in TW5 depends on the nature of the RTSV inoculum used. RT-PCR, sequence, and phylogenetic analyses confirmed that RTSV-VI inoculum differs from RTSV-V inoculum and accurate phenotyping of the resistance to RTSV requires the use of a genetic marker.