We can think of a color filter array (CFA) sensor as being devised this way (I will assume the 'Bayer' pattern).Imagine a final sensor with a sensel pitch of 10 µm.We begin by making three photodetector arrays, each one equipped with a spectral filter of the kinds we describe (rather imprecisely) as 'R', 'G', and B'.They each have photodetectors on a grid of pitch 20 µm in both directions. However, for the 'G' sensor, the detectors are staggered, so that their density per unit area is four times that for the detectors in the 'R' and 'B' sensors.We could use these, with a beam-splitting arrangement, in the manner of the 'three chip' color video camera. Its geometric resolution would be 50 pixels per mm in both vertical and horizontal directions for the 'R' and 'B chips and 100 px/mm for the 'G' chip (this curiosity is complicated to fully describe).

• Aperture Effect In Sampling Pdf Format

Fujifilm camera fans of a few years ago may have already had to do through that mental exercise with regard to their famous 'diagonal array' sensors.​But we don't do that. Rather, we carefully align the three arrays so that no photodetector of one 'sensor' falls in the same spot as a photodetector on another 'sensor' (and the Bayer array allows that). Then we collapse all three sensors onto one (each detector carrying its own little piece of its sensor's 'color filter'). It is important to note here that these errors do not emerge when 'uprez-ing', during demosaicing, the low-geometric-resolution image delivered by a subset of the photodetectors.

The errors were there in the low-geometric-resolution image. Thus to say that 'aliasing in the case of a CFA sensor leads to errors in the interpolation (demosaicing)' is misleading. The errors come from the fact that each layer is 'undersampled' by the 'sparse' collection of photodetectors devoted to that layer.​A bush-league antialising filter?We noted before that the 'virtual lowpass filter' effect caused by a non-infinitesimal sampling window (sampling aperture), while hardly ideal as an antialising filter, could nevertheless do a modest job of that duty, often 'sufficient' in a monochrome or true-color sensor. Will that be true in the case of a CFA sensor?Well, in a typical monochrome sensor, the sampling aperture might be, say, 0.8 times the photodetector pitch, which is 0.8 times the image pixel pitch (and the decline in the frequency response of the virtual lowpass filter, with respect to the Nyquist frequency, is determined by that factor, 0.8).In a Bayer CFA sensor, we might assume a sampling window of 0.8 times the photodetector pitch, which is 0.4 times the image pixel pitch.

As a result, the decline of frequency response of the virtual lowpass filter, with respect to the Nyquist frequency (determined by the pixel pitch), is much slower. And thus the chance that we can get away with just using this response as our antialising filter is much less.Thus the common use of an actual overt antialising filter in cameras with a CFA sensor.Best regards,Doug. There is always a scaling complication, as only a small fraction of the power of the original signal is preserved (the rest being discarded while the sampling gate is closed). In fact, in the limit, as the sampling duration approaches zero (the real premise of our early presentations), the power retained approaches zero, and thus at best the power in the reconstructed waveform has zero power, and thus will have zero amplitude. But we are able to overcome this intellectually.​If, getting practical a bit, we consider sampled pulses of finite duration, there are several forms they can have. Two common ones are:a. They can have exactly the waveform of the original waveform during the entire 'sampled pulse duration' - and have a zero value otherwise.

(This is often called 'natural sampling'.)b. They can have a fixed value during the entire 'sampled pulse duration' - that value being the instantaneous value of the original waveform at some instant, perhaps at the start of the sampled pulse duration - and have a zero value otherwise. (This is often called 'natural sampling'.)Again, in our situation where we immediately feed the train of sampled pulses to the reconstruction filter, we have two different results. With sampling type a, we find that the reconstructed waveform is (other than for the scaling matter I mentioned) identical to the original waveform.

In particular, that means that the relative amplitudes of its different frequency components are the same as for those components in the original waveform. This does not depend in any way on the actual duration of the sampling window and sampled pulses!. With sampling type b, we find that in the reconstructed waveform, the higher frequency components are relatively attenuated compared to lower-frequency components (one manifestation of 'aperture distortion'). The nature of this 'rolloff' depends on the duration of the sampled pulses.Next, in our lecture, we move beyond this model and move to the one that is almost always of actual interest. The value of the original waveform is 'captured' at periodic intervals.w. Those values are given digital numerical representations. The finite precision of that is the cause of an imperfection in reconstructing the waveform, 'quantizing distortion', but I will ignore that here.​x.

The set of those digital representations is stored and/or transported to a distant place.y. Then and/or there, for each original sample, the digital description of its value is used to generate a pules of that amplitude.z.

The train of those reconstructed pulses is fed into a reconstruction filter, out of which comes a waveform that is something like the original waveform.Now, lets look at some possible variations in the details of two of these steps.v. There are two important ways we can 'capture' the value of the waveform:v1. We can (essentially) capture its instantaneous value at precisely the defined sampling instant.v2. We can capture its average value over a small interval, perhaps beginning at the defined sampling instant. Notice I do not mention 'pulses' in this, even though they may exist in the actual circuitry, since this is only a conceptual stage. Thus there are not any such notions as 'natural sampling' or 'flat-top sampling'. Those terms only apply in the model where the pulses generated by the sampler are immediately fed into a reconstruction filter.

It is here that many textbook presentations cause us to go off the rails.​y. There are two important ways we can generate a pulse for each sample value:y1. We can (essentially) generate a pulse of infinitesimal duration. A problem with this is, in the limit, that pulse train itself has infinite bandwidth, and is thus hard to handle with real circuitry, and the train contains no energy, so it is hard to do anything with it.y2. We can generate a pulse of significant duration.Now, if we do v2, the effect on end-to-end reconstruction of the waveform is as if we had a lowpass filter with a certain response ahead of the sampling process.

This is one manifestation of the concept of 'aperture distortion'.Then is we do y2, the result on end-to-end reconstruction of the waveform is as if we had a lowpass filter with a certain response after the reconstruction filter. This is another manifestation of the concept of 'aperture distortion'.The two together affect the 'frequency response' of the whole end-to-end process of converting the waveform, and we may well wish to introduce, at the end, an equalizer that will restore 'uniform' frequency response to the whole process.How does this apply to digital photography?In digital photography, where we represent (here a two-dimensional) 'waveform' through sampling and then digital representation, there are some key differences from the models I described above. But the basic principles indeed apply.The sampling is essentially done in mode v2, since the sampling 'window' is that of the acceptance area of the photodetector, which we intentionally make as large as possible.In reconstruction, the process is essentially y2, since for each pixel value, we generate a spot of almost the pixel width in size in our display.Now where is the reconstruction filter?

There is none. Instead, we rely on the virtual low-pass filter created by the finite 'reconstructed pulse duration' (here the spot size) to be a bush-league reconstruction filter. (This is the same as using the detector window size to be a bush-league antialiasing filter.) The shortcomings of this ploy are the cause of another ailment in image reconstruction called 'display aliasing'. But that is for another time.Best regards,Doug.

Franz Laermer. Kai Kolari, in, 2015 21.5.3 High Aspect RatiosDRIE enables high aspect ratio structures.

Holes and trenches with 10:1 to 20:1 aspect ratios can be fabricated, and pillars with aspect ratios up to 50:1 have been demonstrated: 300 nm feature size, 15 μm structure height 89. These high aspect ratio structures are usually limited to one feature size and shape, or else RIE-lag will affect results.In the fabrication of high aspect ratio trenches, the effective etch rate is reduced with a rising aspect ratio of the trenches. There is a changing balance between passivating and etching species, and a trend toward more passivation with the higher aspect ratios is reached during the etch. In addition, the amount of ions reaching the trench floor slowly diminishes for reasons of aperture effects at the trench opening, in combination with the angular distribution of the ions. As a consequence, profiles tend to develop positive slopes and trenches end up tipping when their aspect ratios reach values of higher than typically 20:1.Given the condition of having trenches all within a similar range of widths, there is a solution to this problem: During the progress of the etch, the process recipe is adapted stepwise or continuously 90,91 (e.g., to reduce the amount of passivation in the process). For example, passivation cycle time or passivation gas flow can be ramped down steadily.

As an alternative, etching cycle time or etching gas flow can be ramped up steadily. Although other options, like source power, bias power, or pressure ramping do exist, changing cycle times is the most obvious parameter ramping strategy for affecting the etch:deposition-balance in a predictable and straightforward manner. With the use of parameter ramping, trenches of greater than 50:1 aspect ratio can be fabricated, while keeping the sidewalls straight and vertical.In hard disk drive actuators, stiffness of the actuator head can be increased by using more complex geometries instead of simple beams. For example, DRIE is essential in the fabrication of 5 μm thick, 200 μm high beams 92. Figure 21.15. Si DRIE pillar structures: (a) liquid chromatography column 93; (b) bead trapping device 94; (c) DNA separation matrix 89.Out-of-plane microneedles make use of DRIE 95,96, especially when hollow needles for injection or suction are needed, while wet etching is suited for simple needles and tips.

Needle density can be increased by using DRIE. Electrospray tips have been microfabricated by various means, but DRIE offers means to integrate multiple nozzles with through-wafer fluidic inlets. Through-wafer DRIE limits the minimum nozzle size to ca.

10 μm nozzle diameter 75. Ozevin, in, 2014 10.4.2 Acoustic emission sensorAE are transient stress waves released within a material due to sudden stress–strain change caused by newly formed damage surfaces. The passive nature of the AE method requires sensors with high sensitivity and low noise level. The other sensor requirement is that the sensor surface area should be smaller than the smallest wavelength of the excitation signal to prevent the aperture effect. Typical frequency range used in civil structures is 60–400 kHz.The AE sensors can be resonant or broadband types. The design of a broadband AE sensor is achieved by keeping the damping of the sensor high, which provides the fast damped response of the sensor causing a reduction in the amplitude of the output signal.

Typical AE sensors are made of piezoelectric ceramics. However, it is not possible to design low frequency miniature AE sensors using conventional piezoelectric bulk ceramics. Buku latihan untuk prasekolah di. There are three types of MEMS AE sensors designed in the literature: capacitive, piezoelectric, and optical.

Ozevin et al. (2006) designed and characterized the first capacitive AE sensors in the literature fabricated in the commercial three-layer polysilicon surface micromachining process (Multi-User-MEMS-Processes (MUMPs)). Each transducer is a parallel plate capacitor with one plate free to vibrate, thereby causing capacitance change which creates an output signal in the form of a current under bias voltage. While the sensors could detect the AE events due to crack development in weld metal, their sensitivities are about fifty times less than conventional piezoelectric AE sensors ( Ozevin et al., 2006). The current output i(t) in a capacitive transducer for a solid coupled system excited by x(t) is ( Ozevin, 2005).

10.13 i t = V DC ε o A g 2 dx t dtThe squeeze film damping of thin films influenced the dynamic response x(t) of the microstructure. Harris et al. (2011) designed an improved capacitive AE sensor for out-of-plane sensing using the open-grill approach to reduce squeeze film damping.

They also designed a comb drive sensor for in-plane sensing; however, the design limitations of the micromachining process used in this research causes coupling of in-plane and out-of-plane sensing for comb drive design. Saboonchi and Ozevin (2013a) designed and manufactured capacitive type MEMS AE sensors using an electroplating technique.

The sensors are manufactured by MetalMUMPs process, which allows higher aspect ratio geometry than surface micromachined sensors. The MEMS AE sensors in this study operate at atmospheric pressure, and have signal-to-noise ratio comparable to bulk type piezoelectric sensors at their resonant frequencies.Feng and Tsai (2010) designed a piezoelectric AE sensor made of multilayer polyvinylidene fluoride (PVDF) using a micro-embossing fabrication technique. The sensor has an operational frequency range of 10 kHz–1.4 MHz. Schoess and Zook (1998) implemented a resonant micro-beam as an AE sensor. Under an excitation signal caused by propagating elastic waves, a micro-beam made from polysilicon vibrates, which is converted to mechanical signal using a focused laser system.

The MEMS design approach developed in this study can be combined with fiber optic systems for a compact AE sensor design. Richard Sheng, in, 2019 7.7.1 General DesignEquipment locationTwo pieces of equipment performing completely different functions may interfere with each other, based on their signal characteristics, operational frequencies, etc.One of the most important factors in achieving EMC is the bonding and grounding of electrical and electronic equipment cases to the conductive airframe.The most effective termination is a 360-degree peripheral bond between the braid and a connector back shell. The peripheral termination configuration ensures a low-impedance electrical bond and, therefore, potential EM coupling is minimized.Use of composite structures on aircraft has become more widespread to reduce weight. In addition to the aperture effects, the use of composites in certain areas of the aircraft can result in other coupling concerns. Specifically, if a carbon composite structure is located on the aircraft skin, the partial conductivity of the material may allow current to flow through.

However, because of its high resistance, the resulting voltage drop across the structure can be significant. This voltage can induce a similar voltage on cable bundles installed under the composite structure. If the potential voltages are too high for certification due to composite usage, additional protection is necessary. The protection technique may be incorporated on the wiring (such as shielding), or on the composite material (such as by “metallizing”). Such protection could negate the weight saved by using the composite in the first place, or even add weight over that which would be had if the structure were metal.When lightning strikes an aircraft, the current flows through the airframe. Typically, many structural members make up the electrical path for the current. Designers should ensure that the method(s) used to join these members (for example, fasteners) will properly complete the electrical path.

Otherwise, ionization of the air gap between members occurs, possibly creating an arc and damaging the materials. One must also ensure the method of joining the structure members can carry the lightning current. Otherwise, damage to the interfaces of the members can occur.As aircraft incorporate more electronic parts and make greater use of nonmetallic structural materials, systems become more vulnerable to the effects of electromagnetic fields and sudden electric surges associated with lightning strikes.

As a result, certification requirements are becoming tougher, while standards are still evolving in this field. Therefore, cognizant engineers must be very alert to certain issues including: (1) internal and external environments, (2) qualification and certification, (3) design techniques, and (4) when to visit your friendly EMC lightning engineer.

In aircraft design we consider three different elements of the electromagnetic (EM) environment. 1.Electromagnetic interference and compatibility. Electromagnetic interference (EMI) refers to the electromagnetic emissions of a system or systems.

Electromagnetic compatibility (EMC) refers to the condition that no component on the aircraft creates electric or magnetic effects that cause any other component to fail to operate properly. 2.High intensity radiated fields (HIRF). High intensity radiated fields refers to an EM environment generated by high power transmitters, such as the Voice of America.

These fields can be extremely strong and there is a real potential for adverse effects. Lightning strikes of aircraft occur regularly. Strong currents flow through the airframe during a strike. These currents can damage external structures and create transients in wiring of electrical/electronic systems. Transient currents can flow throughout the aircraft. Therefore, all structures and safety-related electrical/electronic systems must be properly protected.When addressing the electromagnetic environment of an airplane there are two zones, external and internal, to be considered.The external electromagnetic environment consists of two components: HIRF and lightning. The envelope test can be used as a qualitative measure of large-signal bandwidth (sometimes referred to as full-power bandwidth) and slewing ability in flash A/D converters.

In this test a full-scale sine wave at a frequency slightly higher than the Nyquist frequency, or one-half the sampling rate, is used as the input signal to the A/D. This relationship between the sampling clock and input signal produces two digitized outputs for each period of the input, offset in phase by approximately 180°, as shown in Fig. 6-12. Relationship between clock and input for envelope test.By using a reconversion D/A, or plotting the digitized outputs collected from a logic analyzer, the “envelope” will appear as two low-frequency sine waves, which are amplitude modulating the input frequency, 180° out of phase. Though not truly AM signals, the output waveforms will be the difference between the input frequency f in and the Nyquist rate f CLK/2.

As a measure of large-signal response and overload recovery, this test presents a worst-case situation to the A/D when the peaks of the input are being sampled. At these points the A/D must slew to opposite extremes of its reference range on consecutive samples.

Aperture Effect In Sampling Pdf Format

Non-symmetrical slewing ability of the A/D is indicated by asymmetry on either side of the peaks of the envelope.At the zero crossing of the envelope (which should coincide with midscale for the A/D), noise effects, aperture uncertainty, slewing limitations, and sparkle codes may become evident. Sampling at this point exposes the comparators to the fastest slewing portion of the input signal. Nonsymmetry in the comparator’s response will be seen by comparing alternate zero crossings. As the input crosses the threshold of the MSB transition, aperture errors or poor thermometer decoding between adjacent comparators may cause an output glitch or “sparkle code.”.

If an A/D performs satisfactorily in an envelope test, the concept can be extended to the beat-frequency test as a further measure of input signal bandwidth. The beat frequency is generated by the aliasing of a signal offset slightly in frequency from the sampling rate, as shown in Fig. 6-13. For this test a single tone will be observed at the difference frequency between the input and the sampling clock. The equation above can be used to assure that all codes are sampled by changing the f CLK/2 term to f CLK in the calculation of Δ f. Relationship between clock and input for beat-frequency test.If a reconversion D/A is used to observe the A/D’s output on an oscilloscope, attenuation due to the internal bandwidth limitations of the A/D can be directly measured in real time during the beat and envelope tests. By calibrating the oscilloscope graticule against the output of a full-scale low-frequency signal, loss of dynamic range with an aliased signal at the same frequency will be obvious.

Of course, the same measurement can also be made by examining the extent of the digital codes that are acquired from a logic analyzer. Figure 5 illustrates the effect of undersampling a real image. At the top of Fig. 5a, we see a jagged edge along the crest of the dune. In addition, close inspection of the ripples in the sand reveals what appear to be fine lines oriented at 90° to the ripples. Both these artifacts are due to undersampling.

5b, we see that the energy in the Fourier transform oriented along a fine line at about 75° from the positive U axis has folded back, creating short diagonal line segments in the second and fourth quadrants. This spectral component corresponds to the edge of the crest. In addition, the more diffuse cloud of energy oriented at 45° to the positive U axis has folded back, creating clouds in the upper left and lower right corners of the spectrum. This spectral component corresponds to the ripples in the sand. Effect of undersampling an image of a sand dune: (a) undersampled image, and (b) the magnitude of its Fourier transform.The Nyquist condition may be stated more generally in a necessary and sufficient form: If and only if the support of G( u, v) does not exceed an area of size UV, g( x, y) may be reconstructed from its samples taken on a rectangular lattice at interval (1/ U, 1/ V). The interpolating function will be the inverse CSFT of the indicator function for the support region, scaled by 1/ UV.

Now let's consider the effect of the aperture indicated by (25). If the CSFT P( u, v) of the aperture rolls off at frequencies outside Ω U, V, the aperture will attenuate any frequencies in the continuous-parameter image g( x, y) outside Ω U, V, thereby suppressing aliasing. This desirable effect is known as prescan bandlimitation or antialiasing. On the other hand, if P( u, v) rolls off, i.e.P( u, v) 0 for all frequencies ( u, v) ∈ Ω U, V. This effect may be compensated by replacing (28) with.