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Calculation of IMAGE/MENA geometric factors and conversion of images to units of integral and differential flux
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Image of FIG. 1.
FIG. 1.

(Color online) Overview of the IMAGE spacecraft and the MENA instrument. (a) The MENA instrument mounted on the IMAGE spacecraft. The spin axis is vertically upward in this photograph. (b) The MENA instrument in the laboratory with protective covers in place. (c) Schematic illustration of the MENA collimators and transmission grating assembly relative to the coordinate system used throughout the article. (d) Schematic illustration of a single MENA head. The various components shown in (c) and (d) are not to scale.

Image of FIG. 2.
FIG. 2.

(Color online) (a) Definition of coordinate system used to compute the projected area. (b) Schematic showing area overlap in the or “imaging” direction. The start-byte aperture is shown projected down to the detector plane at three different angles. The left and right cases illustrate partial overlap while the central case illustrates complete overlap. As increases, the area of overlap will first increase linearly from zero to a maximum “plateau” value and then decrease linearly from the maximum value back to zero. [E.g., see Fig. 4(b).] (c) Area overlap in the or “collimated” direction. In (b) and (c), the relative sizes of the start and stop regions are not to scale.

Image of FIG. 3.
FIG. 3.

Calibration measurements of the start byte and stop byte to position mappings. The straight line fit to the start position vs start byte curve shown in (a) was used for all three heads. Head-dependent cubic polynomials were used to fit the stop position vs stop byte data. The cubic polynomial fit for head 2 is shown in (b).

Image of FIG. 4.
FIG. 4.

Projected area [i.e., expression (18)] vs for and a start-byte value of 7 in head 2. (a) Curves for every fourth stop byte from 0 to 128 have been over plotted. (b) A zoomed in view for stop bytes 53 and 54 only. Note that constant, flat-topped plateaus occur in the shadow area, , vs profiles whenever the parallel-projected start-byte aperture and the stop-byte “detector” area have different sizes. This combined with the trigonometric factors in expression (18) give rise to the variability in the upper envelope in (a). Note that the variability can be fairly complicated because over some angular ranges the start width is less than the stop width while for other angular ranges the reverse is true.

Image of FIG. 5.
FIG. 5.

(Color online) Exploded view of the MENA collimators and transmission gratings. Shown are the curved collimator plates, the coarse nickel support mesh, the gold bars and the fine nickel support grid. Note that the coarse mesh is the bottom-most layer with the nickel and gold grating structure resting on top of it. Figure is not to scale.

Image of FIG. 6.
FIG. 6.

Scanning electron micrographs (SEMs) of a nonflight-unit MENA transmission grating. (a) and (b) The gold bars are the vertically aligned structures and the fine nickel supports are the much larger horizontal bars. The rectangular holes were intentionally cut with an ion beam so that the dimensions of the bars could be measured. (c) Same as (a) but with dimensions overlayed. (d) A magnified view of the gold bars near the upper edge of the hole shown in (b).

Image of FIG. 7.
FIG. 7.

(Color online). Schematic illustration of collimating structures with (a) rectangular and (b) trapezoidal cross sections. The transmission probabilities are given in (b) and (d).

Image of FIG. 8.
FIG. 8.

(Color online) (a, b) Defining the “barrel” geometry in terms of intersecting cylinders. (c) The transmission probability that results when the incident parallel rays are tangent to the cylindrical sidewalls. (d) When , the rays are no longer tangent to the cylindrical sidewalls. In this regime, the problem reduces to that of the rectangular cross section shown in Fig. 7.

Image of FIG. 9.
FIG. 9.

(a) SEM showing a corner region of the coarse nickel mesh. The fine nickel bars are the medium-sized horizontal structures and the much smaller gold grating bars can be seen as vertical white stripes below them. Note that the coarse mesh is the same height as the fine nickel supports and therefore does not significantly alter the transmission characteristics. (b) Dimensions and transmission efficiency, , of the coarse triangular nickel support mesh (not to scale).

Image of FIG. 10.
FIG. 10.

Angular dependence of the transmission probabilities for the various collimating structures in MENA. (a) As a function of for the curved collimator plates. Note that is dependent on both and for the collimator plates. (b) As a function of for the curved collimator plates. (c) As a function of for the gold transmission grating bars assuming they have barrel-shaped cross sections. Note that is independent of in this case. (d) As a function of for the fine nickel supports. Note that is independent of in this case. (e) Total transmission probability as a function of . Curves for , , , , , , , , and are shown. (f) Total transmission probability as a function of . Curves for , , , , and are shown.

Image of FIG. 11.
FIG. 11.

(Color) Geometric factors for heads 1, 2, and 3. Each curve represents a different start-byte value (4–14). The geometric factors for start-byte values of 0–3 and 15 are all zero because those byte values do not map to physical locations in the entrance aperture. Similarly, start-byte values of 4 and 14 give lower G, because they map to regions near the edge of the entrance aperture and are somewhat truncated as a result.

Image of FIG. 12.
FIG. 12.

(Color) (a) Main window of the IMAGE/MENA interactive data processing tool. Data from a storm interval on October 5, 2000 is shown. The ENA images are (effectively) integral flux images for . The broad cyan colored regions are due to ENAs emitted from the plasma sheet. (b) Projected version of the image shown in (a).

Image of FIG. 13.
FIG. 13.

(Color) Count rate vs polar angle and integral flux (count-rate/G) vs polar angle (for ) for six different time periods. The contribution from each head is color coded (head 1 is green, head 2 is yellow, head 3 is blue). Many spins were used (except for the July 16 example) in order to reduce counting noise.

Image of FIG. 14.
FIG. 14.

(Color online) Time-of-flight (TOF) byte to energy mapping at two different polar angles. TOF bytes used for the requested energy bands as a function of polar angle bin. Note that the actual and implied by these groupings of bytes is what should be used in the flux conversion formula—not the requested and .

Image of FIG. 15.
FIG. 15.

(Color) Variation of energy and as a function of polar angle and requested energy band. For a given energy band, the actual (green points) and (purple points) will vary with polar angle. The white points are the polar angle distribution of the raw counts (210 spins of data from October 4, 2000). All quantities are plotted in arbitrary units and the scaling is different for all panels. However, to get a sense of the energy scaling, the two horizontal red lines drawn on each panel indicate the requested energy range (e.g., for the upper right hand panel and for the lower right hand panel). Note that for all but the case, the and “curves” are discontinuous functions of polar angle. This is due to the fact that different groups of time-of-flight-byte bins need to be used at different polar angles. As can be seen in the raw count rate distributions, introduction of discontinuities in the data is the main consequence of this inconsistency. But notice also, that gaps in coverage can occur when becomes small as is the case for the panel.

Image of FIG. 16.
FIG. 16.

(Color) Interactive graphical tool illustrating how differential flux images can be created without energy binning.

Image of FIG. 17.
FIG. 17.

(Color) (a) Differential flux images at eight different energies constructed from IMAGE/MENA direct-events data acquired during a storm on June 18, 2001. (b) An example of polar-angle “blooming” in an image acquired on October 14, 2000. The units for flux in both panels are number/.


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Table I.

Hardware byte down sampling.

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Table II.

MENA flight unit transmission gratings

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Table III.

MENA collimator dimensions and transmission efficiencies.

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Table IV.

Calculated effective areas at for head 2.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Calculation of IMAGE/MENA geometric factors and conversion of images to units of integral and differential flux