Simple Wave-Optical Superpositions as Prime Number Sieves.

We encode the sequence of prime numbers into simple superpositions of identical waves, mimicking the archetypal prime number sieve of Eratosthenes. The primes are identified as zeros accompanied by phase singularities in a physically generated wave field for integer valued momenta. Similarly, primes are encoded in the diffraction pattern from a simple single aperture and in the harmonics of a single vibrating resonator. Further, diffraction physics connections to number theory reveal how to encode all Gaussian primes, twin primes, and how to construct wave fields with amplitudes equal to the divisor function at integer spatial frequencies. Remarkably, all of these basic diffraction phenomena reveal that the naturally irregular sequence of primes can arise from trivially ordered wave superpositions.

A method of dosimetry for synchrotron microbeam radiation therapy using radiochromic films of different sensitivity.

This paper describes a method of film dosimetry used to measure the peak-to-valley dose ratios for synchrotron microbeam radiation therapy (MRT). Two types of radiochromic film (manufactured by International Specialty Products, NJ, USA) were irradiated in a phantom and also flush against a microbeam collimator (beam width 25 microm, centre-to-centre spacing 200 microm) on beamline BL28 B2 at the SPring-8 synchrotron. Four experiments are reported: (1) the HD-810 and EBT varieties of radiochromic film were used to record 'peak' dose and 'valley' (regions in between peaks) dose, respectively; (2) a stack of HD-810 film sheets was microbeam-irradiated and analysed to investigate a possible dose build-up effect; (3) a very high MRT dose was delivered to HD-810 film to elicit a measurable valley dose to compare with the result obtained using broad beam radiation; (4) the half value layer of the beam with and without the microbeam collimator was measured to investigate the effect of the collimator on the beam quality. The valley dose obtained for films placed flush against the collimator was approximately 0.2% of the peak dose. Within the water phantom, the valley dose had increased to between 0.7 and 1.8% of the peak dose, depending on the depth in the phantom. We also demonstrated, experimentally and by Monte Carlo simulation, that the dose is not maximal on the surface and that there is a dose build-up effect. The microbeam collimator did not make an appreciable difference to the beam quality. The values of the peak-to-valley ratio reported in this paper are higher than those predicted by previously published Monte Carlo simulation papers.