Mathematical And Computational Methods For Freeform Optical Shape Description

Slow-servo single-point diamond turning as well as advances in computer controlled small lap polishing enable the fabrication of freeform optics, specifically, optical surfaces for imaging applications that are not rotationally symmetric. Freeform optical elements will have a profound importance in the future of optical technology. Orthogonal polynomials added onto conic sections have been extensively used to describe optical surface shapes. The optical testing industry has chosen to represent the departure of a wavefront under test from a reference sphere in terms of orthogonal φ-polynomials, specifically Zernike polynomials. Various forms of polynomials for describing freeform optical surfaces may be considered, however, both in optical design and in support of fabrication. More recently, radial basis functions were also investigated for optical shape description. In the application of orthogonal φ-polynomials to optical freeform shape description, there are important limitations, such as the number of terms required as well as edge-ringing and ill-conditioning in representing the surface with the accuracy demanded by most stringent optics applications. The first part of this dissertation focuses upon describing freeform optical surfaces with φ-polynomials and shows their limitations when including higher orders together with possible remedies. We show that a possible remedy is to use edge-clusteredfitting grids. Provided different grid types, we furthermore compared the efficacy of using different types of φ-polynomials, namely Zernike and gradient orthogonal Q-polynomials. In the second part of this thesis, a local, efficient and accurate hybrid method is developed in order to greatly reduce the order of polynomial terms required to achieve higher level of accuracy in freeform shape description that were shown to require thousands of terms including many higher order terms under prior art. This comes at the expense of multiple sub-apertures, and as such iv computational methods may leverage parallel processing. This new method combines the assets of both radial basis functions and orthogonal phi-polynomials for freeform shape description and is uniquely applicable across any aperture shape due to its locality and stitching principles. Finally in this thesis, in order to comprehend the possible advantages of parallel computing for optical surface descriptions, the benefits of making an effective use of impressive computational power offered by multi-core platforms for the computation of φ-polynomials are investigated. The φ-polynomials, specifically Zernike and gradient orthogonal Q-polynomials, are implemented with a set of recurrence based parallel algorithms on Graphics Processing Units (GPUs). The results show that more than an order of magnitude speedup is possible in the computation of φ-polynomials over a sequential implementation if the recurrence based parallel algorithms are adopted

Acceleration of computation of phi-polynomials

The benefits of making an effective use of impressive computational power offered by multi-core platforms are investigated for the computation of phi-polynomials used in the description of freeform surfaces. Specifically, we devise parallel algorithms based upon the recurrence relations of both Zernike polynomials and gradient orthogonal Q-polynomials and implement these parallel algorithms on Graphical Processing Units (GPUs) respectively. The results show that more than an order of magnitude improvement is achieved in computational time over a sequential implementation if these recurrence-based parallel algorithms are adopted in the computation of the phi-polynomials

Comparative assessment of freeform polynomials as optical surface descriptions

Slow-servo single-point diamond turning as well as advances in computer controlled small lap polishing enables the fabrication of freeform optics, or more specifically, optical surfaces for imaging applications that are not rotationally symmetric. Various forms of polynomials for describing freeform optical surfaces exist in optical design and to support fabrication. A popular method is to add orthogonal polynomials onto a conic section. In this paper, recently introduced gradient-orthogonal polynomials are investigated in a comparative manner with the widely known Zernike polynomials. In order to achieve numerical robustness when higher-order polynomials are required to describe freeform surfaces, recurrence relations are a key enabler. Results in this paper establish the equivalence of both polynomial sets in accurately describing freeform surfaces under stringent conditions. Quantifying the accuracy of these two freeform surface descriptions is a critical step in the future application of these tools in both advanced optical system design and optical fabrication

ANTIMICROBIAL ACTIVITY OF VARIOUS EXTRACTS OF OCIMUM BASILICUM L. AND OBSERVATION OF THE INHIBITION EFFECT ON BACTERIAL CELLS BY USE OF SCANNING ELECTRON MICROSCOPY

The antimicrobial activities of chloroform, acetone and two different concentrations of methanol extracts of Ocimum basilicum L. were studied. These extracts were tested in vitro against 10 bacteria and 4 yeasts strains by the disc diffusion method. The results indicated that the methanol extracts of O. basilucum exhibited the antimicrobial activity against tested microorganisms. While the chloroform and acetone extracts had no effect, the methanol extracts showed inhibition zones against strains of Pseudomonas aeruginosa, Shigella sp., Listeria monocytogenes, Staphylococcus aureus and two different strains of Escherichia coli. The cells of microorganisms, which were treated and untreated with plant extracts, were observed by using the scanning electron microscope. It was observed that the treated cells were damaged

Determining of Relationship Between Weed Seedbank in Soil and Weed Flora in Potato Areas

Bu çalışmada, Van Gölü ve Çevresi önemli patates ekiliş alanlarından Erciş ve Ahlat’ta topraktaki yabancı ot tohumlarının yoğunlukları, rastlanma sıklıkları ve bunların floraya yansıması araştırılmıştır. Erciş ve Ahlat patates ekiliş alanlarında 0-25 cm’lik toprak derinliğinde Amaranthus retroflexus L. ve Portulaca oleracea L. tohumlarının en yoğun türler olduğu saptanmıştır. Topraktaki tohum rezervinin floraya yansıma oranının Erciş’te sadece 2007 yılında %1.2; bunun dışında %1’den düşük olduğu belirlenmiştir.In this study it was investigated in order to determine density of weed seeds and reflection to flora at Ercis and Ahlat. The most common weed species were determined as to Amaranthus retroflexus L. and Portulaca oleracea L. in dept 0-25 cm of soil reservoir at Ercis and Ahlat fields. The ratio of reflection to flora of seed reservoirs in soil is determined lower than 1% as well. But this ratio in Ercis is found 1.2% in 2007

Synthesis of an injectable heparin conjugated poloxamer hydrogel with high elastic recoverability for temporomandibular joint disorders

The temporomandibular joint (TMJ) is commonly affected during fundamental oral activities, reducing the quality of life. Herein, we synthesized a heparin-conjugated poloxamer hydrogel (HEP) as a thermo-responsive injectable hydrogel for the treatment of TMJ disorders. While the gelation temperature of synthesized HEP (25% [w/v]) was 29.8-30.0 degrees C, there was a slight difference between loss and storage modulus. HEP decreased the friction of the TMJ, thus requires less energy during load-bearing jaw movement in comparison to POL. Moreover, the oscillation test dependent on strain ranges from 0.01% to 1000% validated that POL and HEP3 hydrogels showed a similar critical strain of about 5.6%. The total elastic recovery percentage of HEP3 (53.50%) was higher than POL (45.55%), indicating a better recovery of the deformed hydrogel structure. Along with the suitable viscoelastic properties for temporomandibular cavity, both hydrogels increased the proliferation of fibroblasts (L929) and chondrocytes (ATDC5) (cell viabilities were above 100%). However, newly synthesized HEP induced differentiated cell proliferation of chondrogenic cells at increasing concentrations up to 0.0156 mg/mL (p < 0.0001) compared to POL and the control group. The promising rheological properties and effects on chondrogenic cell proliferation of injectable heparin-conjugated hydrogel make them candidates for intra-articular injections used for the treatment of TMJ

Genetic diversity and relationship analysis among accessions of Aegilops ssp in Turkey using amplified fragment length polymorphism (AFLP) markers

Amplified fragment length polymorphism (AFLP) DNA markers were used to assess the genetic diversity and relationships between 55 accessions of genus Aegilops, including the species Aegilops triuncialis L. (UUCC), Aegilops geniculata Roth (MMUU), Aegilops cylindrica Host (CCDD) and Aegilops umbellulata Zhuk (UU). The samples were collected from Aegean region and East Anatolia, Turkey. 16 AFLP selective primer combinations generated a total of 3200 polymorphic amplification products. 50 Aegilops accessions were analyzed using the data analysis software, unweighted pair-group method arithmetic average (UPGMA) method and numerical taxonomy and multivariate analysis system (NTSYSpc-2.02k). The similarity index coefficients were calculated according to simple matching coefficient. Using 16 AFLP primer combinations, species from Aegean region and east Anatolia were clustered as four major groups. Aegilops species having U genome clustered together and A. cylindrica host was out grouped

Modeling Air-flow in the Tracheobronchial Tree using Computational Fluid Dynamics

In this paper, we present a biomechanical framework to model air-flow inside the bronchus and deformations across the tracheobronchial tree, pipeline for the simulator, theory and initial steps to realize this framework on a highly parallel graphical processing unit (GPU). We discuss the main challenges expected and encountered to date. By using computational fluid dynamics (CFD) and computational solid dynamics (CSD) principles, we propose a numerical simulation framework that includes a biomechanical model of the tracheobronchial tree to simulate air flow inside the tree, on GPU in real-time. The proposed 3D biomechanical model to simulate the air inside the lungs coupled with a deformation model of the tracheobronchial tree, expressed through fluid-structure interaction, can be used to predict the transformations of the voxels from a 4D computed tomography (4DCT) dataset. Additionally, the proposed multi-functional CFD and CSD based framework is suitable for clinical applications such as adaptive lung radiotherapy, and a regional alveolar ventilation estimation

Evaluation of Four Adult Visceral Leishmaniasis Cases

Leishmania infantum is the species responsible for visceral leishmaniasis [(VL), kala-azar], which is observed sporadically mainly in pediatric age groups in the Aegean, Mediterranean and Central Anatolian regions of Türkiye. The aim of this study is to evaluate the diagnosis, clinic, laboratory results and treatments of four adult patients with VL who applied to our hospital. The patients were referred to our hospital to investigate hematological malignancy. In the study, the data of four patients (three men, one woman; age range: 30-40 years) who were diagnosed with VL and treated in the infectious diseases clinic of our hospital between January 2022 and April 2022 were evaluated retrospectively. The diagnosis of VL was made according to appropriate clinical and physical examination findings, biochemical and serological tests (indirect fluorescent antibody test and rK39 rapid antigen test) and polymerase chain reaction (PCR) results, as well as the presence of amastigote forms of the parasite in bone marrow samples. Serology positivity was found in all patients, and bone marrow positivity was found in two patients. According to the results of RT-PCR in all patients, it was determined that the species causing the disease was L. infantum/L. donovani. Initially, the most common symptoms were fever, fatigue, and abdominal distension. None of the patients had an immunosuppressive condition. It was understood that all the patients lived in the rural area of Syria’s Idlib province. Hepatosplenomegaly, increased erythrocyte sedimentation rate, anemia, leukopenia and thrombocytopenia were found in all patients. The patients were treated with liposomal amphotericin-B (L-AMB). One patient did not come for follow-ups, the other three patients were found to have completely recovered in their follow-up. No recurrence was observed in any of the patients. In conclusion, VL should be considered in patients who apply to health institutions with complaints of fever, hepatosplenomegaly, increased erythrocyte sedimentation rate, anemia, leukopenia and thrombocytopenia