Time Varying Signals Part A Chemistry 838

Transcription

1 Part A Chemistry 838 Thomas V. Atkinson, Ph.D. Senior Academic Specialist Department of Chemistry Michigan State University East Lansing, MI 88 Table of Contents TABLE OF CONTENTS... TABLE OF TABLES... TABLE OF FIGURES ACQUISITION AND DISPLAY OF DATA THE SINE FUNCTION Lissajou Figures Two Sine Waves Lissajous Figures Sine Wave versus Sawtooth..... DATASETS Single Variable Two Variables Many Variables TIME BASED ACQUISITION SCENARIOS Acquisition Timing Schemes When Does Acquisition Begin Studying Multiple Signals Analog vs. Digital Acquisition Strategies Multiple Acquisitions of a Varying Signal Triggered Acquisitions ACQUISITION HARDWARE ANALOG DIGITAL METHODS OF TIME SHARING... September, Version 7A.

2 Table of Tables.3.. Multiplexing Alternate Mode Chopped Mode HOW TO CHOOSE RASTER DISPLAYS RANDOM ACCESS DISPLAYS CRT ANALOG OSCILLOSCOPE TIME SHARING THE BEAM THE ROLE OF THE OSCILLOSCOPE OSCILLOSCOPE (Y VERSUS TIME EXAMPLES) ASYNCHRONOUS SWEEP, WITH AND WITHOUT BLANKING SYNCHRONIZED SWEEP TRIGGERED SWEEP RASTER DEVICES (TV, MONITOR) ON THE CRT TIMING EXAMPLES Black and White Black and White (Multiple Frames Example) Gray Scale Gray Scale (Multiple Frames Example) Interlaced RASTER IMAGES Black and White Gray Scale Interlaced CRT MODES SUMMARY GRAPHICAL REPRESENTATIONS FULL BITMAP GRAYSCALE COLOR... 7 Table of Tables TABLE - TWO VARIABLE MEASUREMENTS... TABLE - TRIG, POSITIVE SLOPE PARAMETERS...7 TABLE 3 - ACQUISITION PARAMETERS...8 TABLE - ACQUISITION PARAMETERS...9 TABLE 5 - ACQUISITION PARAMETERS...3 TABLE 6 - ACQUISITION PARAMETERS...33 TABLE 7 - SIGNAL PARAMETERS... TABLE 8 - OSCOPE PARAMETERS...3 TABLE 9 - OSCOPE PARAMETERS... September, Version 7A.

3 Table of Figures TABLE OSCOPE PARAMETERS...5 TABLE OSCOPE PARAMETERS...6 TABLE - RASTER GRAPHICS DEVICE...68 Table of Figures FIGURE - SINE FUNCTION...5 FIGURE - LISSAJOU FIGURE (:)...7 FIGURE 3 - DISPLAYING TWO SINE WAVES OF EQUAL FREQUENCY...8 FIGURE - DETERMINATION OF PHASE ANGLE...9 FIGURE 5 - LISSAJOUS FIGURES...9 FIGURE 6 PROJECTION OF A SINE AND SAWTOOTH... FIGURE 7 - TYPICAL EXPERIMENTAL MEASUREMENT... FIGURE 8 - TIME COURSE OF TWO VARIABLES... FIGURE 9 - MULTICHANNEL ANALYZER...3 FIGURE - ACQUISITION WINDOW...5 FIGURE - EQUAL ACQUISITION INTERVALS...6 FIGURE - VARIED ACQUISITION INTERVALS...6 FIGURE 3 EXPONENTIAL ACQUISITION INTERVALS...6 FIGURE - MULTIPLE SIGNALS...6 FIGURE 5 - HIGH DUTY CYCLE SIGNAL...7 FIGURE 6 - LOW DUTY CYCLE SIGNAL...8 FIGURE 7 - LOWER DUTY CYCLE SIGNAL...8 FIGURE 8 - ORIGINAL SIGNAL... FIGURE 9 - ACQUISITION A... FIGURE - ACQUISITION WINDOWS... FIGURE - ACQUISITION B... FIGURE - OVERLAY A, B, C... FIGURE 3 - ACQUISITION C... FIGURE ORIGINAL SIGNAL... FIGURE 5 ACQUISITION A... FIGURE 6 ACQUISITION WINDOWS... FIGURE 7 ACQUISITION B... FIGURE 8 OVERLAY A, B, C... FIGURE 9 ACQUISITION C... FIGURE 3 - ORIGINAL SIGNAL...3 FIGURE 3 - ACQUISITION A...3 FIGURE 3 - ACQUISITION WINDOWS...3 FIGURE 33 - ACQUISITION B...3 FIGURE 3 - OVERLAY A, B, C...3 FIGURE 35 - ACQUISITION C...3 FIGURE 36 ORIGINAL SIGNAL... FIGURE 37 ACQUISITION A... FIGURE 38 ACQUISITION WINDOWS... FIGURE 39 ACQUISITION B... FIGURE OVERLAY A, B, C... FIGURE ACQUISITION C... FIGURE - ORIGINAL SIGNAL...5 FIGURE 3 - ACQUISITION A...5 FIGURE - ACQUISITION WINDOWS...5 FIGURE 5 - ACQUISITION B...5 FIGURE 6 - OVERLAY A, B, C...5 FIGURE 7 - ACQUISITION C...5 FIGURE 8 - SIMPLE TRIGGER (LEVEL/SLOPE)...6 FIGURE 9 - TIME COURSE OF A TRIGGERED ACQUISITION...6 September, Version 7A.

4 Table of Figures FIGURE 5 - SIGNALS...7 FIGURE 5 - TRIGGERED, POSITIVE SLOPE - RESULTANT...7 FIGURE 5 - SIGNALS...8 FIGURE 53 - RESULTANT DISPLAY...8 FIGURE 5 - SIGNALS...9 FIGURE 55 - RESULTANT DISPLAY...9 FIGURE 56 - SIGNALS...3 FIGURE 57 - RESULTANT DISPLAY...3 FIGURE 58 - SIGNALS...3 FIGURE 59 - RESULTANT DISPLAY...3 FIGURE 6 - SIGNALS...33 FIGURE 6 - RESULTANT DISPLAY...33 FIGURE 6 - SINGLE PULSE...3 FIGURE 63 - CIRCULAR BUFFER...38 FIGURE 6 - PRE, MID, POST TRIGGERS...38 FIGURE 65 - ANALOG ACQUISITION SYSTEMS...39 FIGURE 66 - DIGITAL ACQUISITION SYSTEMS... FIGURE 67 - DIGITAL OSCILLOSCOPE WITH COMPUTER CONNECTION... FIGURE 68 - MULTIPLEXED ADC... FIGURE 69 - CATHODE RAY TUBE...8 FIGURE 7 STEERING THE BEAM WITH VOLTAGE...9 FIGURE 7 STEERING THE BEAM WITH CURRENT...9 FIGURE 7 BEAM POSITION VS. DEFLECTION VOLTAGE...9 FIGURE 73 BEAM POSITION VS. DEFLECTION CURRENT...9 FIGURE 7 - DOT INTENSITY VS. BEAM FLUX...5 FIGURE 75 - PHOSPHOR PERSISTENCE...5 FIGURE 76 - OSCILLOSCOPE SCHEMATIC...5 FIGURE 77 - MULTI-TRACE OSCILLOSCOPE SCHEMATIC...5 FIGURE 78 - SIMPLE SWEEP...5 FIGURE 79 - SWEEP WITH Z-AXIS BLANKING...53 FIGURE 8 - ASYNCHRONOUS SWEEP...5 FIGURE 8 - SYNCHRONIZED SWEEP...55 FIGURE 8 - SIMPLE TRIGGER (LEVEL/SLOPE)...56 FIGURE 83 - TIME COURSE OF A TRIGGERED SCOPE...56 FIGURE 8 - TRIGGERED SWEEP...57 FIGURE 85 - TRIGGERED SWEEP II...58 FIGURE 86 - ABRAHAM LINCOLN ( PIXELS PER INCH)...69 FIGURE 87 - ABRAHAM LINCOLN (6 PIXELS/INCH)...69 FIGURE 88 - GRAYSCALE...69 FIGURE 89 - ABRAHAM LINCOLN DETAIL ( PIXELS PER INCH)...69 FIGURE 9 - ABRAHAM LINCOLN DETAIL ( PIXELS PER INCH MAGNIFIED)...7 FIGURE 9 - THE RESPONSE OF THE HUMAN EYE TO LIGHT...7 FIGURE 9 - RESOLUTION ELEMENT FOR COLOR CRT...7 September, Version 7A.

5 Acquisition and Display of Data. Acquisition and Display of Data This section examines issues impacting the acquisition and display of data. This generalized discussion has applicability to analog oscilloscopes, digital oscilloscopes, and computerized data acquisition... The Sine Function The mathematical sine function is a periodic function of two variables that has great importance in analog and digital electronics, and in experimental science and will be used in many sections of this document. In many sections of this document the sine function will be used as an example signal. The concepts developed using the sine function as an example can be easily extrapolated to more complicated signals. Indeed, Fourier says that all periodic functions is the sum of sine functions. The following is a brief review of the sine function. The sine function is a function of one dependent and one independent variable. In one manner of description, the dependent variable (y) is the y-component of a vector of length A, A = in Figure, that is rotating around the point at the tail of the vector as illustrated in the left side of Figure. The independent variable is the angle, θ, of rotation. The right side of Figure is a plot of three cycles of y versus θ. If the vector is rotating at a constant velocity ω, then θ = ωt. In this latter case the x-axis of the plot could be expressed in time as well. 3 π / ( ) π/ (9 ) π/ (5 ). Sine.cdr 9-Aug-7 π (8 ) y V p V pp 5 π / (5 ) 7 π / (35 ) 3 π / (7 ) (Periods) (Degrees) π π 3π π 5π 6π Radians Figure - Sine Function The sine function is described in mathematical notation as follows. y( t) = Asin( θ + φ) If the vector is rotating at a constant velocity ω, then θ = ωt. y( t) = Asin( ωt + φ) y ( t) = Asin(πft + φ) September, Version 7A.

6 Acquisition and Display of Data π πt ( ) sin( φ π y t = A t + ) = Asin( ( t + tφ )) p p p p = / f ω = πf πtφ φ = πftφ = p Where: y is the amplitude of the signal at time t A is the amplitude of the sine wave ω is the frequency of the sine wave in radians per unit time f is the frequency of the sine wave in number of cycles per unit time p is the period of the sine wave in units of time φ is the phase angle (or simply the phase) t φ is the time of the offset of the beginning of the cycle of one sine wave to the beginning of a second sine wave of the same frequency. September, Version 7A.

7 Acquisition and Display of Data... Lissajou Figures Two Sine Waves , ,7 7 Sine,6, Sine , , Sine Lissajou.cdr 3-Sep-7 Sine Figure - Lissajou Figure (:) September, Version 7A.

8 Acquisition and Display of Data Figure 3 - Displaying Two Sine Waves of Equal Frequency September, Version 7A.

9 Acquisition and Display of Data... Lissajous Patterns - Phase Angle Measurement PhaseAngle_.cdr c b a sin φ = c/b Figure - Determination of Phase Angle... Lissajous Figures - Different Frequencies Figure 5 - Lissajous Figures Horizontal to Vertical Frequencies a.) : b.) : c.) :5 d.) : September, Version 7A.

10 e.) 5:3 Acquisition and Display of Data... Lissajous Figures Sine Wave versus Sawtooth Figure 6 Projection of a Sine and Sawtooth Figure 6 illustrates how the trajectory of the dot on an analog oscilloscope can be determined given the signals applied to the horizontal and the vertical channels. If one were to carry out this procedure for longer periods of time, one sees that if the two signals are periodic, the trajectory is reproducible and the dot retraces the same closed path... Datasets The choice of a scenario used to acquire data depends on a large number of factors. For instance, is the desired function periodic or aperiodic? Is the sample stable, i.e. can the experiment be reproduced? Will a single acquisition of data be sufficient, or will multiple acquisitions be needed, say, to average out the noise or to study the changes in the sample as a function of time?... Single Variable In a few situations, the results of an experiment is a set of measurements that yield a set of single variables. The measurements can be made at any time, i.e., there are no constraints as to when. Furthermore, there are no other variables are considered. An example is flipping coins in a probability experiment. The only information needed whether each flip (y i ) results in heads or tails y, y, y, y3, y, L yn 3, yn, yn n Equation September, Version 7A.

11 ... Two Variables Acquisition and Display of Data Many experiments produce datasets of two variables such as the typical spectrum seen in Figure 7. Classically, the measurements of the individual x,y pairs are made at anytime, merely set x and measure y. An example is when the spectrum of a stable sample is acquired with a spectrometer with manually selected wavelength. Another example is the classical titration where the independent variable is the volume of titrant added up to that point in the titration. The dependent variable is the state of the indicator, e.g. the ph of the solution, or the color of the indicator at that point. ( x, y),( x, y), L( xn, yn ),( xn, yn) Equation GeneralMeasurement.opj - TwoLines - 9-Aug-7.5. Depend ent V ariable Independent Variable Figure 7 - Typical Experimental Measurement Table lists a number of two variable experiments of importance to the modern chemist. Table - Two Variable Measurements Measurement Independent Variable Dependent Variable Absorption Spectrometry Wavelength Absorption of incident light Emission Spectrometry Wavelength Emitted light intensity EPR, NMR Magnetic field Absorption of incident electromagnetic radiation Voltametry Voltage across the Electrochemical Cell Current through cell Kinetics Concentration of a given species Titration Volume of titrant State of the indicator Single Crystal Crystallography Orientation of detector in 3 space X-ray intensity Mass spectrometry Magnetic field Ion current September, Version 7A.

12 Acquisition and Display of Data An important variant of this type experiment occurs when the independent variable is time. An example of this is the kinetic experiment where the concentration of a chemical species is to be measured as a function of time. These experiments produce datasets of the form shown below. ( t, y),( t, y), L( tn, yn ),( tn, yn) Equation 3 Another example is the typical modern spectrometer where the output wavelength of the monochromator can be scanned over a region of wavelengths, usually linearly with time. As the wavelength is scanned, the amplitude of the output signal, e.g. absorbance, transmittance, or light intensity, is automatically recorded. This precludes the need for the operator to manually set the wave length, make a reading, change the wave length, etc. ( x( t), y( t)), ( x( t), y( t)), L( x( tn ), y( tn )),( x( tn), y( tn)) Equation where x(t i ) is the wavelength at time t i, y(t i ) is the intensity of the signal at time t i. The actual dataset acquired is typically of the form of Equation 3. The conversion of the data set to the form of Equation is achieved with the parameters of the wave length sweep, i.e. the initial wavelength and the rate of change of wavelength...3. Many Variables The next level of complexity is the case where there are two dependent variables (y,i and y,i ) and one independent variable (x i ). Figure 8 is an example of this type experiment where the intensity of light emitted from a sample is simultaneously measured at two wave lengths providing the monitoring of two different species in the sample. In this case, time is the independent variable. The intensity of the signal at wavelength λ and the intensity of the signal at wavelength λ the dependent variables. ( x, y,, y,),( x, y,, y,), L( xn, y, n, y, n ),( xn, y, n, y, n ) Equation 5 Intensity Figure 8 - course of Two Variables September, Version 7A.

13 Acquisition and Display of Data More dependent variables (y j,i where j = to the number of dependent variables) are possible. (, x, y,, y,, y3,, L)( x, y,, y,, y3,, L), L,( xn, y, n, y, n, y3, n, L),( xn, y,, y, n, y3 n, L) ti, y, i, y, i, y3, i, L, y8, i, y9, i, a, a, a3, L, a8, a ) where i = to the number of ( 9 Equation 6 Another example of one independent variable and multiple dependent variables is found in Figure 9 where an incident beam of radiation or particles hits a piece of material that disperses the beam into beams at various angles relative to the incident beam. The multiple detectors can simultaneously measure the intensity of the dispersed beams. The measurements could be repeated as a function of time. The dataset would consist of a set of points as follows. points Equation 7 The a j in the above equations are parameters, e.g. the angle of the dispersed beam relative to the input beam and are constants for the experiment. The dispersive element is the sample being studied in some cases. In others, the incident beam has passed through the sample being studied before reaching the dispersive element. MultiChannelDetectors.cdr 3-Aug-7 y y y 3 y y 5 y 6 Detector y 7 y 8 Light/ particle beam y 9 y y Dispersion Element y 3 y y y 9 y 8 y7 y 6 Figure 9 - Multichannel Analyzer Figure 9 illustrates a setup consisting of a collection of discreet detectors. CCD, and other similar type, array detectors consist of as many as million detectors implemented on a single integrated circuit and are also capable of capturing an array of dependent variables a simultaneously. y 5 September, Version 7A.

14 Acquisition and Display of Data In general, a dataset may have multiple independent variables and multiple dependent variables, and multiple parameters. ( 3 x, i, x, i, x3, i, L y, i, y, i, y3, i, L, a, a, a, L, ak ) k = the number of parameters where i =to number of points and Equation 8 An example of a dataset with multiple independent variables is found in single crystal crystallography. The dataset for this experiment consists of three independent variables (h, k, l) which define a location on a sphere centered at the crystal being studied. The dependent variable (I) is the intensity of diffracted X-rays at that location. The analysis of such a dataset can produce the structure of the molecule making up the crystal. ( h, k, l, I),( h, k, l, I ),( h3, k3, l3, I3), L,( hn, kn, ln, I n ),( hn, k n n n.3. Based Acquisition Scenarios, l, I ) Equation 9 This section will focus on the acquisition of datasets consisting of time as the independent variable and one or more dependent variables. This is by far the most common variety acquisition of experimental data. The interface performs the final domain conversion, i.e. converts the quantity being measured into digital form, if this has not already happened, and gates the results into the computer to be stored or analyzed. This section focuses on various hardware systems used as interfaces acquiring the quantities and recording the values for later analysis. Typically, sets of observations, i. e. measurements of the values of various parameters of the system, are made by the experimenter as the state of the system changes. Thus, the process results in a set of observations that can be represented as follows. y (t ), y (t ),, y q (t ) y (t ), y (t ),, y q (t ) y (t n ), y (t n ),, y q (t n ) In the above representation, measurements of the values, y i, of q parameters of the system are made at n different times. is always an independent variable in experimentation since the measurements have to be made in real time. The times, t i, of the observations may often be correlated with some other parameter. As an example, if the observation is the intensity of the light coming out of a monochromator and the wavelength is being scanned over time, the time values can be related to the values of the wavelength. The result is a spectrum. September, Version 7A.

15 Acquisition and Display of Data StandardWindow.cdr -JUL-997 y max Δy y min t min t max (x min ) ( x max ) Δt (Δx) Figure - Acquisition Window An experiment can be thought of a series of measurements of one or more dependent variables with time as the independent variable. An acquisition window, i. e. Figure, describes how the data is acquired for a given dependent variable. In essence, the measurement process is the discovery of the set of points on the grid of the acquisition window that are the closest to the signal or parameter being measured. Of course, what actually happens is that the grid point nearest the physical parameter for t min is determined and then that for the next time increment, etc. sequentially in time across the window. The typical goal is to optimize the window so that the signal being acquired fills the window giving the maximum resolution possible. The window is defined by the choices of the parameters t min, t max, Δt, y min, y max, and Δy. The choices are constrained by the needs of the experiment and the abilities of the acquisition system..3.. Acquisition Timing Schemes Figure shows a constant Δt, which is the most common strategy. Figure contains an example of an acquisition using equal acquisition intervals. Figure 3 and Figure suggest other, nonlinear strategies that may be desirable. The ultimate goal is to gather the best information possible about the signal of interest. More data points are usually desired for the portions of a signal that are changing more rapidly, hence, the non-linear cases could be considered in such cases. September, Version 7A.

16 Acquisition and Display of Data Signal base Signal 8 8 base Figure - Equal Acquisition Intervals Figure - Varied Acquisition Intervals 9 8 Signal base 8 7 Signal base Signal Figure 3 Exponential Acquisition Intervals Figure - Multiple Signals.3.. When Does Acquisition Begin Another important consideration is the specification of t min, i.e. when does the acquisition of information begin. Typically, the acquisition of a signal is to begin at a particular time. The identification of when that time, i.e. the trigger event, has occurred causes the acquisition to begin Studying Multiple Signals Figure illustrates a frequent need to acquire more than one signal at a time. A common approach is to use a multiplexed ADC which results in the timing shown in Figure Analog vs. Digital The implied quantized nature of the measurements in this discussion is slanted toward the use of Analog to Digital Converters to make the measurements. However, the use of analog September, Version 7A.

17 Acquisition and Display of Data oscilloscopes, analog recorders, and manual recording to acquire a set of data is similar. In those cases the Δt and Δy are the horizontal and vertical resolutions of the analog device. As with all measurements, the best results occur for these devices when the signal being measured fills the oscilloscope display, the width of the recorder, etc. That is, the best results are when the signal of interest fills the acquisition window Acquisition Strategies High Duty Cycle Signal Figure 5 - High Duty Cycle Signal September, Version 7A.

18 Acquisition and Display of Data Low Duty Cycle Signal Figure 6 - Low Duty Cycle Signal Lower Duty Cycle Signal Figure 7 - Lower Duty Cycle Signal September, Version 7A.

19 Acquisition and Display of Data.3.6. Multiple Acquisitions of a Varying Signal This section examines issues with multiple acquisitions of a periodic signal. The goal is, almost always, to have the multiple windows (y k (i ), i = to the number of points per set) be super imposable, i.e. y j (i) and y k (i) correspond to the same relative point in the respective acquisitions. These following examples all use noise free signals in order to more clearly illustrate the issues revolving around the registration of multiple data sets Synchronized Acquisitions Figure 8 through Figure 7 illustrate five examples of scenarios for acquiring the same sine wave signal (A PtoP = 8 units, p = 5 time units). Each case consists of three acquisition windows (A, B, C). The goal is for each scenario to produce three data sets that are exactly registered in the independent variable (time). The concepts illustrated here can be extended to an arbitrary number of acquisitions. Figure 8 through Figure 3 illustrate a case where three acquisitions of the signal are made and the resultant data sets are exactly registered with one another and exact constructive addition is possible. This is a consequence of the width (5 time units) of the acquisition window being an exact multiple of the period of the signal being measured. The three acquisition windows follow immediately after one another and begin at t =, 5, and time units. Figure through Figure 9 illustrates a second acquisition scenario that again produces three sets of data that are exactly registered in the independent variable. This registration is shown by the fact that the three signals exactly overlay one another as shown in Figure 8. Again this is a consequence of the width (5 time units) of the acquisition window being an exact multiple of the period of the signal being studied. However, in this case the acquisition windows do not follow immediately after each other but they do start at the same relative point (t =,, and time units) in the cycles of the signal being studied. Figure 3 through Figure 35 illustrates an acquisition scenario that again produces three sets ( time units each) of data that are exactly registered in the independent variable as shown by the fact that the three signals exactly overlay one another as shown in Figure 3. This coherence is a consequence of each acquisition window starting at the same relative point (t =,, and 5 time units) in the cycles of the signal being studied. In this case the acquisition windows do not follow immediately after each other and are at irregular intervals. Notice that these data sets differ from the above due to a different span of time ( time units). Figure 36 through Figure illustrates a case where the acquisition scenario fails to produce appropriately registered data sets. This failure can be seen in Figure where three different traces are seen, one from each acquisition window. Notice that the width (5 time units) of the acquisition window is the same as in the Figure 8 through Figure 3 and Figure through Figure 9 cases. However, the starting points (t =, 7, time units) for the acquisition windows do not fall on the same point within the cycles of the signal. Figure through Figure 7 illustrates another case where the acquisition scenario fails to produce appropriately registered data sets. This failure is seen in Figure 6 where three different traces are seen, one from each acquisition window (A, B, C). In this case, the three acquisition windows follow immediately after each other. However, the width (6 time units) of the September, Version 7A.

20 Acquisition and Display of Data acquisition window results in the starting points (t =, 6, time units) for the windows to not fall on the same relative points of the cycles of the signal. September, Version 7A.

21 Synchronized Acquisition and Display of Data (Absolute) 3 5 (Absolute) Figure 8 - Original Signal Figure 9 - Acquisition A Window A Window B Window C (Absolute) Figure - Acquisition Windows Figure - Acquisition B (Relative to Acquisition Window) 3 5 (Absolute) Figure - Overlay A, B, C Figure 3 - Acquisition C September, Version 7A.

22 Synchronized Acquisition and Display of Data (Absolute) 3 5 (Absolute) Figure Original Signal Figure 5 Acquisition A Window A Window B Window C (Absolute) (Absolute) Figure 6 Acquisition Windows Figure 7 Acquisition B (Relative to Acquisition Window) 3 5 (Absolute) Figure 8 Overlay A, B, C Figure 9 Acquisition C September, Version 7A.

23 Synchronized 3 Acquisition and Display of Data (Absolute) 3 (Absolute) Figure 3 - Original Signal Figure 3 - Acquisition A Window A Window B Window C (Absolute) -6 3 (Absolute) Figure 3 - Acquisition Windows Figure 33 - Acquisition B (Relative to Acquisition Window) (Absolute) Figure 3 - Overlay A, B, C Figure 35 - Acquisition C September, Version 7A.

24 Synchronized Acquisition and Display of Data (Absolute) 3 5 (Absolute) Figure 36 Original Signal Figure 37 Acquisition A Window A Window B Window C (Absolute) (Absolute) Figure 38 Acquisition Windows Figure 39 Acquisition B (Relative to Acquisition Window) (Absolute) Figure Overlay A, B, C Figure Acquisition C September, Version 7A.

25 Synchronized 5 Acquisition and Display of Data (Absolute) (Absolute) Figure - Original Signal Figure 3 - Acquisition A Window A Window B Window C (Absolute) (Absolute) Figure - Acquisition Windows Figure 5 - Acquisition B (Relative to Acquisition Window) (Absolute) Figure 6 - Overlay A, B, C Figure 7 - Acquisition C September, Version 7A.

26 Acquisition and Display of Data.3.7. Triggered Acquisitions Trigger_.cdr T P T P T P V trigger source Trigger Source T N T N T N T - Trigger Event (Trigger Slope = Positive) P T - Trigger Event (Trigger Slope = Negative) N Figure 8 - Simple Trigger (Level/Slope). Trigger sources: a. Internal (Channel, Channel, ) Signal of interest b. External c. Line T T T Trigger_.cdr A D S F A D S F A D S F A A - Trigger is armed and the acquisition is ready to begin T - Trigger Event occurs and the acquisition sequence begins D - Post Trigger Delay (if any) is in process S - Sampling occurs, acquisition of the data is in progress. F - House keeping: process data, prepare for next acquisition sequence. Figure 9 - Course of a Triggered Acquisition September, Version 7A.

27 Acquisition and Display of Data Triggered Acquisition Positive Slope Oscope_Triggered_.opj - Signals - 6-Aug-7 Table - Trig, Positive Slope Parameters 5 5 Trigger Slope AcqSig Trigger Level Initial Delay Triggered TrigArmed Post Trigger Delay Flyback 75 Number of Samples 3 Oscope_Triggered_.opj - Sample - 6-Aug-7 Positive SLope TrigOn Signal Signal Figure 5 - Signals (Relative to the Acquisition Window) Figure 5 - Triggered, Positive Slope - Resultant September, Version 7A.

28 Acquisition and Display of Data Triggered Acquisition Negative Slope Table 3 - Acquisition Parameters Oscope_Triggered_.opj - Signal3-6-Aug-7 AcqSig Triggered TrigArmed TrigOn Signal - - Signal Oscope_Triggered_.opj - Sample3-6-Aug-7 Signal Parameter Value Trigger Slope - Trigger Level Initial Delay Post Trigger Delay Flyback 75 Number of Samples Figure 5 - Signals (Relative to the Acquisition Window) Figure 53 - Resultant Display September, Version 7A.

29 Acquisition and Display of Data Triggered Acquisition Negative Slope, Post Trigger Delay Oscope_Triggered_.opj - Signals - 6-Aug-7 Table - Acquisition Parameters 5 5 Parameter Value AcqSig Trigger Slope - Trigger Level Triggered Initial Delay Post Trigger Delay 6 TrigArmed Oscope_Triggered_.opj - Samples - 6-Aug-7 Flyback 75 Post Trigger Delay TrigOn Signal Trigger Event Acquisition begins Signal - - Figure 5 - Signals (Relative to Acquisition Window) - Figure 55 - Resultant Display September, Version 7A.

30 Acquisition and Display of Data Triggered Acquisition Positive Slope Oscope_Triggered_3.opj - SignalAll - 7-Aug Signal September, Version 7A.

31 Acquisition and Display of Data AcqSig Triggered TrigArmed Oscope_Triggered_3.opj - Signal - 7-Aug-7 3 Parameter Value Trigger Slope Trigger Level.5 Initial Delay Post Trigger Delay Flyback 75 Number of Samples 5 Oscope_Triggered_3.opj - Sample - 7-Aug-7 TrigOn Signal Signal Figure 56 - Signals (Relative to Acquisition Window) -6 Figure 57 - Resultant Display September, Version 7A.

32 Acquisition and Display of Data Oscope_Triggered_3.opj - Signal3-7-Aug-7 Table 5 - Acquisition Parameters 3 Parameter Value AcqSig Trigger Slope Trigger Level Triggered Initial Delay Post Trigger Delay Flyback 75 TrigArmed Number of Samples 5 TrigOn Oscope_Triggered_3.opj - Sample3-7-Aug Signal Signal Figure 58 - Signals (Relative to Acquisition Window) -3 Figure 59 - Resultant Display September, Version 7A.

33 Acquisition and Display of Data Oscope_Triggered_3.opj - Signal - 7-Aug-7 Table 6 - Acquisition Parameters 3 Parameter Value AcqSig Trigger Slope Trigger Level Triggered TrigArmed Initial Delay Post Trigger Delay Flyback 375 Number of Samples 5 TrigOn Oscope_Triggered_3.opj - Sample - 7-Aug Signal Signal Figure 6 - Signals (Relative to Acquisition Window) Figure 6 - Resultant Display Next we will consider the acquisition of a single pulse, i.e. an aperiodic signal. Figure 6 is an example of a single burst of activity and will be used as an illustration. Two issues can be considered here. The first is how to perform an acquisition that would capture the complete signal. The biggest issue is how you would know when to start the acquisition. September, Version 7A.

34 Acquisition and Display of Data Oscope_Triggered_6.cdr - Signal 9-Aug Figure 6 - Single Pulse September, Version 7A.

35 Acquisition and Display of Data Oscope_Triggered_6.cdr - Signal 9-Aug-7 Parameter Value Triggered AcqSig 3 Trigger Slope Trigger Level 8 Initial Delay Post Trigger Delay Flyback 75 Number of Samples 3 TrigArmed Oscope_Triggered_6.cdr - Sample 9-Aug TrigOn Signal Signal September, Version 7A.

36 Acquisition and Display of Data Oscope_Triggered_6.cdr - Signal3 9-Aug-7 Parameter Value Triggered AcqSig 3 Trigger Slope - Trigger Level Initial Delay Post Trigger Delay Flyback 75 Number of Samples 3 TrigArmed Oscope_Triggered_6.cdr - Sample3 9-Aug TrigOn Signal Signal September, Version 7A.

37 Acquisition and Display of Data Oscope_Triggered_6.cdr - Signal 9-Aug-7 Parameter Value TrigOn TrigArmed Triggered AcqSig 3 Trigger Slope - Trigger Level -6 Initial Delay Post Trigger Delay Flyback 75 Number of Samples Oscope_Triggered_6.cdr - Sample 9-Aug Signal Signal September, Version 7A.

38 Circular Buffers Acquisition and Display of Data Next Data Point is stored here Figure 63 - Circular Buffer y t start t pre t mid t post Figure 6 - Pre, Mid, Post Triggers Acquision_.cdr -Oct- A circular buffer can be used in the acquisition of data. Figure 63 illustrates such a circular buffer; in this case there are locations each of which can contain one data point. The pointer labeled Next Data Point Is Stored Here points to the location where the next item will be stored. In Figure 63 the next item will be stored in location. Once an item is stored in the current location, the pointer is incremented to point to the next location in the clockwise direction. The process can continue without end. Of course, values will be overwritten as the pointer completes a revolution. The pointer always points to the oldest item in the buffer. After the first complete revolution has occurred, a circular buffer with n locations will always contain the last n items stored, e.g. in this case. In the case of data acquisition, the process is started before the window of time during which the features of interest occur. Data points are acquired and the stored in the circular buffer. The acquisition continues until some point in time, e.g. when some trigger event occurs. At that point, the process will be continued for m additional data points where m can be or any number desired. At that time the circular buffer will contain the last n points acquired. Figure 6 illustrates one such case. The process begins at t start. Data points are acquired at equal increments in time and stored in the circular buffer. Three possible trigger events are defined, i.e. t pre, t mid, and t post. In this case the trigger event at t pre could be derived from features on the signal being acquired. The other two trigger events would have to be derived from external sources. There are three variations possible here. First, the pre-trigger is used. The pre-trigger indicates to the controller of the process that more points are to be acquired. The second approach uses the mid-trigger which, in this case, indicates that more points are to be acquired. The third approach uses the post-trigger which indicates that no more data points are to be acquired. As described here, all three approaches would result in the same points being acquired. The choice of which type trigger to use will depend on which features are available on the signal of interest if internal triggering is to be used or what external signals can be used to generate the appropriate trigger events. Notice that the pre-trigger is the type that has been used in this document for the analog oscilloscope and the acquisitions systems prior to this particular section. September, Version 7A.

39 Acquisition Hardware Other variations are possible. For one, if pre-triggering is being used and the controller was set to take 3 more data points after the trigger event occurs, the final data points would correspond to a dataset that begins after a delay of 6 acquisition intervals after the trigger event.. Acquisition Hardware This section provides a brief overview of acquisition hardware. Expanded discussion of this topic occurs later in the course... Analog AcqDisplay_.cdr 3-Aug-7 e Analog Pretreatment Vertical Analog Control Display/Recorder Horizontal Control e Analog Pretreatment Vertical Analog Control Display/Recorder Base e Analog Pretreatment Horizontal Control (A - Simple Single Channel Display) e Analog Pretreatment Vertical Analog Control Display/Recorder e ext Analog Pretreatment Horizontal Control Base e ext Analog Pretreatment (C - Multiple Channel/ X-Y Display) Base (B - Single Channel/ X-Y Display) Figure 65 - Analog Acquisition Systems September, Version 7A.

40 .. Digital Acquisition Hardware AcqDisplay_.cdr 3-Aug-7 Vertical Control Display Horizontal Control e Analog Pretreatment Buffer e Analog Pretreatment Buffer Controller Controller Controller Base Base (A - Single Channel Data Logger) (B - Single Channel Digital Oscilloscope) e Analog Pretreatment Vertical Control Display Horizontal Control Buffer Buffer Controller e Analog Pretreatment Controller Base (C - Two Channel, Individual ADC) Figure 66 - Digital Acquisition Systems e Analog Pretreatment AcqDisplay_3.cdr 3-Aug-7 e Analog Pretreatment Vertical Control Display Horizontal Control Buffer Controller Controller e 3 Analog Pretreatment e 3 Analog Pretreatment Computer Figure 67 - Digital Oscilloscope with Computer Connection September, Version 7A.

41 .3. Methods of Sharing Acquisition Hardware This section examines ways of time sharing ADCs and displays among multiple signals..3.. Multiplexing In this case, one point of one signal is processed, and then a point of the second signal, etc. until all signals have been processed for that time point. Then the next time point is processed for the first signal, and then the next time point for the next signal, etc. This method is the limiting case of the chopped mode. MultiplexADC.cdr -JUL-997 t k t k+ t k+ y k z k+ y(t) z k yk+ y k+ zk+ z(t) Δt acq Δt Data Figure 68 - Multiplexed ADC September, Version 7A.

42 .3.. Alternate Mode Acquisition Hardware Sine.5.5 Voltage Sine.5.5 Voltage Horizontal Voltage. Fraction of sweep Z-Axis = On, = Off Table 7 - Signal Parameters Parameter Sine Sine Amp phase.3 Period.8. Freq.5.5 Offset - September, Version 7A.

43 Acquisition Hardware Vertical Switch Position..8 Channel Vertical Beam Deflection 3 Vertical Position OScope Presentation 3 Vertical Position Fraction of the sweep Table 8 - OScope Parameters Parameter Value Sweep.6 Sweep Flyback. Sweep+Flyback.8 Beam Switch.8 September, Version 7A.

44 Acquisition Hardware.3.3. Chopped Mode Vertical Switch Position..8 Channel Vertical Beam Deflection 3 Vertical Position OScope Presentation 3 Vertical Position Fraction of the sweep Table 9 - Oscope Parameters Parameter Value Sweep.6 Sweep Flyback. Sweep+Flyback.8 Beam Switch.5 September, Version 7A.

45 Acquisition Hardware Vertical Switch Position..8 Channel Vertical Beam Deflection 3 Vertical Position OScope Presentation 3 Vertical Position Fraction of the sweep Table Oscope parameters Parameter Value Sweep.6 Sweep Flyback. Sweep+Flyback.8 Beam Switch. September, Version 7A.

46 Acquisition Hardware Vertical Switch Position..8 Channel Vertical Beam Deflection 3 Vertical Position OScope Presentation 3 Vertical Position Fraction of the sweep Table Oscope parameters Parameter Value Sweep.6 Sweep Flyback. Sweep+Flyback.8 Beam Switch. September, Version 7A.

47 How to choose 3. How to choose If the periods of the signals are much less than the beam switching time, use the alternate mode. If the periods of the signals are much greater than the beam switching time, use the chopped mode. The Tektronix 5 have a fixed chop frequency of Khz or a beam switching time of microseconds.. Raster Displays CRT LCD Plasma 5. Random Access Displays 5.. CRT Many of the figures in this section are from Section 3- and following in "Making the Right Connection" September, Version 7A.

48 Random Access Displays Figure 69 - Cathode Ray Tube Figure 69 illustrates the typical cathode Ray Tube (CRT) used in analog oscilloscopes. Figure 7 is a cross section of the CRT and illustrates how the beam can be steered by applying a voltage across the deflection plates. The analog oscilloscope will have two sets of these plates that are perpendicular to each other and parallel to the axis of the tube. One steers the beam horizontally. One steers the beam vertically. Figure 7 illustrates that an electron beam can also be steered with a magnetic field that is created with a current passing through a coil. This technique is typically used in CRTs used in televisions and computer monitors. Figure 7 and Figure 73 illustrates the relationship between the beam deflection and the deflection voltage and current. Notice that the displacement is linear over a good portion of the screen. Thus, the beam position can be used as a measure of the amplitude of the deflection voltage (or current). September, Version 7A.

49 Random Access Displays Oscope_.cdr +a i filament Filament V deflection -a Figure 7 Steering the Beam with Voltage Oscope_3.cdr +a i filament Filament -a i deflection Figure 7 Steering the Beam with Current Oscope_.cdr +a Oscope_.cdr +a Beam Deflection Beam Deflection -a -a V min V max i min i max V deflection Figure 7 Beam Position vs. Deflection Voltage i deflection Figure 73 Beam Position vs. Deflection Current Figure 7 illustrates the relationship of the intensity of the dot to the intensity of the electron beam. In oscilloscopes, this feature is only used to set the dot intensity to a value that allows easy viewing. However in the cases of televisions and computer monitors, this feature is used to modify the intensity of each small area (pixel) of the image being displayed. More abut this is September, Version 7A.

50 Random Access Displays found in the section on raster devices. Figure 75 shows how the intensity of the dot will decay after the beam is turned off. As you will see shortly, the beam in these devices is never static but is always rapidly moving across the screen of the CRT. Thus, the length of time a given point (pixel) on the screen remains lit after the beam moves on depends on the kinetics of the phosphor used. As you will see, the utility of these CRT devices depends on the image being retraced and the human eye integrating the trace into a stable image. The choice of the speed of the phosphor used will determine the operating characteristics of a given CRT and how it can be used. Oscope_.cdr Oscope_.cdr Beam On Beam Off Intensity of the Light Emitted by the Phosphor (at a given wavelength) Intensity of the Light Emitted by the Phosphor (at a given wavelength) Slow Phosphor Fast Phosphor Electron Beam Intensity (Flux) Figure 7 - Dot Intensity vs. Beam Flux Figure 75 - Phosphor Persistence 5.. Analog Oscilloscope Figure 76 - Oscilloscope Schematic September, Version 7A.

51 5.3. Sharing the Beam The Role of the Oscilloscope Figure 77 - Multi-Trace Oscilloscope Schematic 6. The Role of the Oscilloscope Thus, the oscilloscope is actually two independent voltage measuring devices. Just measure the deflection of the beam in the horizontal direction and this is linearly related to the voltage being applied to the horizontal deflection plates. Likewise the vertical deflection is a measure of the voltage being applied to the vertical deflection plates. If the oscilloscope is carefully constructed and calibrated and the measurement of the deflection is carefully done, one should be able to determine the corresponding voltage to about +- %. One might ask why spend several thousand dollars to buy an instrument that cannot measure voltages with any better resolution than a $5 VOM. The first answer to this question is that the device can be used to simultaneously compare two signals. The second reason is anchored in the September, Version 7A.

52 Oscilloscope (y versus Examples) fact that the beam can be driven from any point within the operational area of the screen to any other point in nanoseconds or even less. Thus, the true role of the oscilloscope is in observing very high frequency signals and/or comparing two time varying signals. 7. Oscilloscope (y versus Examples) The most common application of the oscilloscope is to observe a signal as a function of time. This is achieved by putting the signal being studied on the vertical axis of the scope and putting a standard saw tooth signal on the horizontal axis. Since the amplitude of the saw tooth is linear in time, the horizontal component of the beam position will move across the screen of the CRT linearly in time, i.e. sweep (usually left to right) across the screen linearly in time. The horizontal position of the beam will, hence, be a measure of time. The following sections will examine details of this approach and the exact nature of the function applied to the horizontal axis. 7.. Asynchronous Sweep, With and Without Blanking Sweep_.cdr S F S F S F Max V horizontal Min z-axis (Beam) On Off S - Sweep is on and the beam is moving from left to right F - Flyback - Sweep is returning rapidly to the right of the screen. Figure 78 - Simple Sweep September, Version 7A.

53 Oscilloscope (y versus Examples) Sweep_.cdr S F S F S F Max V horizontal Min z-axis (Beam) On Off S - Sweep is on and the beam is moving from left to right F - Flyback - Sweep is returning rapidly to the right of the screen. Figure 79 - Sweep with z-axis Blanking September, Version 7A.

54 Oscilloscope (y versus Examples) Figure 8 - Asynchronous Sweep The goal of using the oscilloscope in these cases is to make quantitative measurements of the amplitude and time behavior of the signal being studied. As is evident in Figure 8, the resultant display of using a sweep signal that is of a different period from the signal being studied is confusing and unsatisfactory, i.e. making any kind of quantitative measurement would be difficult. September, Version 7A.

55 7.. Synchronized Sweep Oscilloscope (y versus Examples) Figure 8 - Synchronized Sweep Figure 8 illustrates the results of carefully adjusting the sweep time (time to sweep across the screen) to be an integral multiple of the period of the signal being studied. As you can see, the resultant image is much simplified. Since the vertical axis can be calibrated in measured deflection per volt applied to the vertical deflection input, quantitative measurements of the amplitude of the signal being studied can be made. However, since the horizontal sweep rate must be variable to perform the synchronization, quantitative measurement in the horizontal direction is problematic. In addition, parameters of real signals tend to drift leading to a continual need for adjusting the sweep rate to stay in sync. September, Version 7A.

56 7.3. Triggered Sweep Oscilloscope (y versus Examples) Trigger_.cdr T P T P T P V trigger source Trigger Source T N T N T N T - Trigger Event (Trigger Slope = Positive) P T - Trigger Event (Trigger Slope = Negative) N Figure 8 - Simple Trigger (Level/Slope) T T T A S F A S F A S F A Max V horizontal Min z-axis (Beam) On Off A - Sweep is armed and ready to begin T - Trigger Event occurs and the sweep begins S - Sweep is on and the beam is moving from left to right F - Flyback - Sweep is returning rapidly to the right of the screen. Figure 83 - Course of a Triggered Scope Trigger_.cdr September, Version 7A.

57 Oscilloscope (y versus Examples) Figure 8 - Triggered Sweep September, Version 7A.

58 Raster Devices (TV, Monitor) on the CRT Figure 85 - Triggered Sweep II 8. Raster Devices (TV, Monitor) on the CRT This section explores the application of the CRT to televisions and computer monitors. The first section illustrates the time behavior of the horizontal deflection, vertical deflection, and beam intensity signals for a simple case of two lines being displayed on an 8x8 raster. The second section illustrates what the image would look like for the example displays. Modern computer monitors utilize raster of as high as 3x pixels or higher. Thus, this section contains very simplified examples. September, Version 7A.

59 Raster Devices (TV, Monitor) on the CRT 8.. Timing Examples 8... Black and White 5 Vertical Horizontal Beam September, Version 7A.

60 Raster Devices (TV, Monitor) on the CRT 8... Black and White (Multiple Frames Example) 5 Vertical Horizontal Beam September, Version 7A.

61 Raster Devices (TV, Monitor) on the CRT Gray Scale 5 Vertical Horizontal Beam September, Version 7A.

62 Raster Devices (TV, Monitor) on the CRT 8... Gray Scale (Multiple Frames Example) 5 Vertical Horizontal Beam September, Version 7A.

63 Raster Devices (TV, Monitor) on the CRT Interlaced 5 Vertical Horizontal Beam September, Version 7A.

64 Raster Devices (TV, Monitor) on the CRT 8.. Raster Images These examples show how a simple display of two lines (one vertical, one diagonal) would come about in a simple 8x8 raster device. The solid and dotted lines represent the beam path. The beam is only on during the pixel to be lit and these points in time are represented by the ellipses. Thus, the solid and dotted lines would not be seen in the actual display Black and White Raster8x8.cdr -JUL-997 T V Atkinson - Department fo Chemistry - Michigan State University Pixel Vertical flyback Horizontal Line 5 3 Horizontal flyback Raster (8 x 8) Display Black and White September, Version 7A.

65 Raster Devices (TV, Monitor) on the CRT 8... Gray Scale Raster8x8gray.cdr -JUL-997 T V Atkinson - Department fo Chemistry - Michigan State University Pixel Vertical flyback Horizontal Line 5 3 Horizontal flyback Raster (8 x 8) Display Gray Scale September, Version 7A.

66 Raster Devices (TV, Monitor) on the CRT Interlaced Raster8x8grayinterlaced.cdr -JUL-997 T V Atkinson - Department fo Chemistry - Michigan State University Pixel Vertical flyback Horizontal Line 5 3 Horizontal flyback Raster (8 x 8) Display Interlaced Gray Scale The traditional television does not transmit a complete frame (raster) of pixel intensity information at one time. The information is transmitted in two parts, each part containing information in alternative rows. The image is recreated by two interleaved sweeps across the screen. In the figure above one half of the interleave process is represented by the heavy solid line. The other half is represented by the lighter solid line. September, Version 7A.

67 9. CRT Modes Summary CRT Modes Summary Type Horizontal Drive Vertical Drive Beam Drive X-Y plot remote signal source remote signal source on base Oscope (Simplest) local sweep generator (free running) remote signal source on base Oscope (Simple) local sweep generator (free running) remote signal source Blanked on flyback base Oscope (Typical) local sweep generator (Triggered) remote signal source Blanked on flyback and when armed Raster (TV, Monitor) local sweep generator local sweep generator remote source (Beam Intensity contains the visual information for a given point (pixel) in the image being displayed.) The longer the persistence, the lower the refresh rate needed to keep an image visible. The longer the persistence, the slower the motion (i.e. the changes from one frame to the next) can be.. Graphical representations The representation and visualization of D and 3D objects, i. e. graphics, is a major concern in the computer industry. Often graphical representation will provide a more appropriate and efficient method of storing and presenting information. This is a very complicated subject. Methods for representing D and 3D objects are required. 3D objects usually must be represented, i.e. projected, in D. Recreating the color of an object in the presentation is a major topic. In addition, there is a wide variation in the nature, e. g. resolution, color characteristics, speed, etc. of the devices and mechanisms used to present an image that can be viewed by the human. Some aspects of this large area of endeavor will be covered in this section... Full bitmap The vast majority of modern graphical output devices, e.g. CRT, liquid crystal, and other displays, ink jet, laser, and other printers, are raster devices. In such cases, the image is represented by a collection of picture elements (pixels) arranged in a two-dimensional array (raster) as shown in Table. In such representations, graphical elements, e.g. lines, circles... are a set of pixels that are turned "on", against a background of pixels that are "off". In this particular example (3 x 3), a line between 3,5 and 3,5 is thus a set of "darkened" pixels. Computer Graphics: Principles and Practicies, nd edition, James D. Foley, Andries van Dam, Steven K. Feiner, John F. Hughes, Addison-Wesley, 993. September, Version 7A.

68 Graphical representations Cem 9 DataRep -FEB Raster Graphics Table - Raster Graphics Device Notice that horizontal lines and vertical lines are "cleaner" than those at an angle. In this example the pixels have two states, on or off. In general, each pixel can have multiple states such as gray scale or color. September, Version 7A.

69 .. Grayscale Graphical representations Figure 86 - Abraham Lincoln ( pixels per inch) Figure 87 - Abraham Lincoln (6 pixels/inch) % 9% 8% 7% 6% 5% % 3% % % % Figure 88 - Grayscale Figure 89 - Abraham Lincoln Detail ( pixels per inch) September, Version 7A.