Fixed-point numercial-reconstruction for digital holographic microscopy

Abstract

In this Letter, we study the reconstruction of digital holograms of microscopic objects using a fixed-point representation of the numercial-reconstruction process. For different bit levels in our fixed-point reconstruction algorithm, we investigate the errors introduced to both the reconstructed image intensity and the unwrapped quantitative phase information. Experimental results based on a microscopic lens array are provided. © To the best of our knowledge, the numercialreconstruction process that is used both in industry and in the research community employs floatingpoint arithmetic. This Letter addresses the numercial-reconstruction of digital holograms using fixed-point integer arithmetic. We investigate the advantages of such an approach as well as the errors introduced into the quantitative phase. There are two major formats for representing real numbers in bit-sequences of 0s and 1s; floating point and fixed point. Computationally fixed-point arithmetic is less demanding than floating-point arithmetic. Fixed-point devices have a simpler architecture with fewer gates and transistors and thus have smaller cycle clock time and are faster. Additionally fixed-point processors consume less power and generate less heat than floating-point processors and are thus well suited to portable devices where battery life is important. Many embedded systems and handheld units have fixed-point processors. Already there are variants of DHM that do entail some degree of portability in the recording side such as submersibledigital inline microscopes for detection of life forms in remote inaccessible areas [5], holographic on-chip cytometry [6], plankton sampling [7], etc. In scenarios such as these, it is essential to optimize the numercial-reconstruction process so that it uses up as little resources as possible if reconstruction is to be carried out on site.A floating-point bit sequence in binary can be broken into two smaller bit sequences, the signed mantissa and the signed exponent. In the Institute of Electrical and Electronics Engineers floating-point notation [8] a number is represented by N = ͑−1͒ s ϫ m ϫ 2 ͑e−127͒ where s is the sign bit, m is the standard binary number represented by the (normalized) fractional mantissa, and e is the (biased) exponent.Employing a mantissa and an exponent allows the radix point to "float" and thus allows calculations over a wide range of magnitudes. Fixed-point notation on the other hand is simpler. The most common fixed-point notation is the "two's complement." In two's complement, the leading bit of positive numbers is 0 and of negative numbers is 1. The value represented is obtained by assuming that the leftmost bit is negative and then calculating the binary value of the number. The spacing between all the numbers is uniform, and thus fixed-point notation can be viewed simply as a scaled integer. The position of the radix point is fixed. A thorough description of fixed-and floating-point arithmetic can be found in [9].The setup for a typical DHM is shown in Fig. 1. In this st...

Quantization noise and its reduction in lensless Fourier digital holography

“…Recently, the resolution of CCD/CMOS sensors has increased significantly and with it, so, too, has the computational requirement of a digital holographic imaging system. The bandwidth needed for transmission of holograms from one point to another has also increased, and hence compression of digital holograms has been an active area of research [9][10][11][12][13][14][15][16][17][18]. In this context, the quantization of the hologram and the effect on the reconstructed images has been studied before.…”

“…It directly reduces the memory requirement of the hologram, and combined with suitable processing and hardware, can decrease the computational requirement of the digital imaging system [9]. A quantized hologram also can be compressed effectively.…”