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Transformation corrections are a crucial part of photometry, particularly when aiming for high precision and accuracy in measuring stellar magnitudes. In essence, these corrections account for the variations in how different filters and equipment respond to light. Different telescopes, cameras, and filters may not all perfectly match standard photometric systems like the Johnson-Cousins system, leading to small but significant differences in the raw instrumental magnitudes recorded.
Transformation corrections adjust these instrumental magnitudes to a standard system, ensuring that data collected from different observers or equipment can be accurately compared. For example, even two observers using the same type of filter, like a V filter, might still capture slightly different magnitudes due to variations in their equipment. Without transformation, these discrepancies would introduce systematic errors into photometric data.
The transformation coefficients are derived from observations of standard stars, whose magnitudes are well-established. By comparing the instrumental magnitudes of these standard stars to their known catalog magnitudes, one can calculate the necessary corrections. These corrections are applied to the target stars’ magnitudes to bring them into alignment with the standard system
Transformation Coefficients
While Phoranso does not calculate transformation coefficients (TCs) directly, it allows users to apply pre-calculated TCs during photometric processing. There are two types of Transformation Coefficients:
These coefficients account for the transformation of instrumental magnitudes measured through one filter to magnitudes in another filter. They represent the relationship between an object’s color index (the difference in magnitudes between two filters) and the standard color index. These are denoted as Tij, where "i" and "j" refer to the filters used.
Example: Tri is the reciprocal of the least-squares fitted slope of (r-i) plotted versus (R-I), where r and i represent instrumental magnitudes, and R and I standard magnitudes. It measures the change in the standard color index relative to the instrumental color index. In an ideal system, Tri = 1.
- Magnitude (Filter Band) Coefficients
These coefficients transform instrumental magnitudes measured in a specific filter band to standard magnitudes in the same filter band. They are denoted as Ti_ji.
Example: Tb_bv is derived from a plot of (b−B) versus (B−V), where "b" and "B" are instrumental and standard magnitudes in the B filter, and B−V is the standard color index. A more descriptive notation might be Tb_(B-V), Tb_bv is commonly used.
Color sequences
In photometry, a Color Sequence refers to a series of images captured through different filters, arranged in a specific order. For example, a color sequence like B-V-R-B-V-R-B-V-R represents nine images acquired using the B, V, and R filters, in that repeating pattern. The order and repetition of filters within the sequence is important when applying transformation corrections, as they must follow a specific format to ensure accurate grouping and calculation of transformed magnitudes.
For transformation corrections to be applied correctly by Phoranso, the Color Sequence must follow one of two recognized patterns:
- Multiple Filters Repeating in Groups
This format allows sequences where multiple filters are repeated in a consistent order, enabling the images to be grouped under the same group number. Each unique filter is assigned a numerical index based on its position in the group.
A Grouped Sequence consists of images that all share the same group number, indicating they belong to the same observational group. Transformation corrections are only applied to images within the same group. By maintaining this grouping, Phoranso can correctly process the images, facilitating precise application of transformation corrections across your photometric data.
Example 1
A sequence like B-V-R-I-B-V-R-I-B-V-R-I is valid and will produce the grouped sequence:
B1V1R1I1 B2V2R2I2 B3V3R3I3
Example 2
A sequence like B-B-B-V-V-V-R-R-R-I-I-I is also valid and yields the grouped sequence:
B1B2B3 V1V2V3 R1R2R3 I1I2I3
Example 3
A more varied sequence like I-R-B-B-R-I-V-R-B-I-V-V is valid and results in:
I1R1B1B2R2I2V1R3B3I3V2V3
Example 4
The sequence B-V-R-I-B-V-R is invalid because it lacks a consistent grouping of filters. Phoranso will not produce transformed magnitudes for this sequence.
- Dual Filters
This format requires one filter to be followed by one or more instances of another filter, and this pattern must be repeated one or more times.
Example 1
A sequence like I-V-V-I-V-V-V-V is valid. This structure is particularly useful for transforming V magnitudes by regularly inserting new I images. In our example, you acquire an I image followed by several V images, then insert another I image before capturing more V images. This ensures that each set of V measurements is corrected using the most recently obtained I measurement, thereby enhancing the accuracy of the transformation process.
Example 2
Sequences such as I-V-V-V-I-V-R-V-V are invalid since they break the necessary pattern of having one initial filter followed by multiple repetitions of the second filter.
Irregular color sequences
In Phoranso, Color Sequences follow one of two standard patterns: the Multiple Repeating Filters pattern and the Dual Filters pattern.
However, if a color sequence does not fully comply with either pattern, Phoranso will automatically search for the longest possible subset of images within the sequence, that does math one of the two recognized patterns. This subset is then used to apply Transformation Corrections, ensuring that as many images as possible are processed effectively.
Example: the sequence B-V-V-I-B-V-V-V does not conform to either pattern as a whole. The subset of images B-V-V-B-V-V-V matches the Dual Filters pattern. Phoranso will process this subset for Transformation Corrections.
Example: the sequence B-V-R-I-B-V-I does not conform to either pattern as a whole. The subset of images B-V-I-B-V-I matches the Multiple Repeating Filters pattern, and Phoranso will process this subset.
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