HADAMARD SPECKLE REDUCTION FOR MILLIMETER WAVE IMAGING Irina Jaeger, Johan Stiens, Gaetan Koers, Gert Poesen, and Roger Vounckx Vrije Universiteit Brussel Department of Electronics Laboratory for Micro- and Photonelectronics Pleinlaan 2, Brussels 1050, Belgium Received 24 February 2006 ABSTRACT: Millimeter wave imaging technology makes possible im- aging of phenomena, which are inaccessible to visible light, but suffer from speckles, produced by coherent sources. We report a 50% speckle reduction, measured with a free-space vector network analyzer over the full W-band. Our experiments demonstrate how Hadamard mask oper- ates as a tunable filter. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 1722–1725, 2006; Published online in Wiley Inter- Science (www.interscience.wiley.com). DOI 10.1002/mop.21747 Key words: mm-wave imaging; speckle; Hadamard transform 1. INTRODUCTION Free-space active millimeter-wave imaging employs THz radiation to illuminate the object and the signals reflected from the object are collected by the receiver. Possible applications of millimeter waves are closely related to the transmitter/receiver frequency band. According to a general trend [1], W-band (75–110 GHz) supports an imaging of concealed objects and medical imaging. Optimum imaging operating frequency corresponds to the mini- mum of tan , providing both good spatial resolution and penetra- tion. For many materials, this optimum frequency is about 100 GHz and corresponding spatial resolution is of the order of a few millimeters in free space. There are a number of advantages of active imaging over the passive: resolution and contrast can be increased by using/adjusting wavelength, polarized light, and an- gles of incidence; and possibility of noise elimination and as a result, possibility of signal detection below the noise level. But a number of problems have to be tackled to achieve these properties. Coherent light propagating through a random medium will pro- duce fluctuations in intensity due to interference of the multiple scattered waves. So the coherence level of mm wave sources has to be substantially decreased and speckles have to be reduced. The correlation function of speckle patterns produced at different wavelengths has been studied under different system conditions— both with reflected and transmitted light [1– 6]. It was shown that speckle patterns decorrelate with increasing object roughness or with increasing difference in the wave numbers. Various optical speckle suppression techniques have been studied to measure surface roughness properties [6]. Considerable effort has been also made in investigating speckle contrast versus surface roughness [5, 6]. In [7, 8], Hadamard codes were demonstrated for imaging spectrometer setting an absoluter standard for binary digital en- coding: other binary digital codes may exist, but they can not be better. Speckle contrast was efficiently reduced by an optical free-space Hadamard diffuser [4, 5]. Contrast can be calculated systematically for all types of surfaces and all ranges of wave- lengths, including millimeter waves. Following Goodman [2, 3], we will use a speckle contrast as a measure of the speckle. This is defined as the ratio of the standard deviation  to the mean of the speckle intensity I, and its value is between 0 and 1. It was demonstrated that a speckle contrast was efficiently reduced by optical free-space Hadamard mask [4, 5]. The Hadamard transform is a square matrix M = 2 integer over (-1, 1), where each row and each column are perfectly uncorrelated. Rows and columns, considered as vectors, are orthagonal. The Hadamard diffuser gives a maximum speckle reduction M -1/2 with a minimum number of distinct phase patterns  ij = 0 or  ij = . Since the detector is only sensitive to intensities, it detects fields as a superposition from the electromagnetic fields E ij on an amplitude basis. If the coherent intensity is I coh = |  ijE ij | 2 , the speckle intensity with Hadamard transform becomes S = 1 m  m |  ij H ij E ij | 2 =  ij | E ij | 2 = I incoh , where H ij = expi ij  and m is number of pixels. We estimated effectiveness of the Hadamard transform if the phases are not exactly 0 or . Simulations (see Fig. 1) show an improvement of speckle contrast under 2  2 Hadamard transform. The improve- ment starts almost linear with the /2-phase. For the frequency 100 GHz, the depth of Teflon (n = 1.44) is d = 4.9 mm, according to the formula 2/ air - 2/ air nd =  and this phase /2 corresponds to the frequency 50.1 GHz. It means that the Had- amard transform imaging is not so sensitive to monochromatic signal fluctuations as was expected from [4, 5] and may be also used for the broadband applications. 2. FABRICATION OF MM-WAVE HADAMARD DIFFUSER There are two possibilities for the masks: one- and two-layered systems [8]. The one layered system only consists of a single movable mask. In the two-layered system there is one fixed and one movable mask, blocking certain pixels of the fixed mask. The mask is usually a uniform arrangement of square holes in opaque material. The holes define the visible part of an image pixel [5, 8]. We fabricated our mask by micro-drilling a Teflon sample. We started with four 2  2 Hadamadrd matrixes H 1 =  1 1 1 1  , H 2 =  1 - 1 - 1 1  , H 3 =  1 - 1 1 - 1  , H 4 =  1 1 - 1 - 1  , Figure 1 Simulated original speckle contrast over phases between 0 and  (red, circles), speckle contrast under 2  2 Hadamard transform with not precise -phase (blue, stars) and with non precise 0-phase (blue, dots). [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com] 1722 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 48, No. 9, September 2006 DOI 10.1002/mop