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Share-Based Compensation - Restricted stock units related to the plan 2019 (Details) - USD ($) | 12 Months Ended
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Sep. 30, 2022 | Sep. 30, 2021 | Sep. 30, 2020
Share-Based Compensation |  |  |
Share-based compensation expense | $ 345,000 | $ 341,000 | $ 177,000
Restricted Stock Units |  |  |
Share-Based Compensation |  |  |
Restricted stock units outstanding ( in shares) | 7,886 | 0 | 0
Restricted Stock Units | Stock Based Incentive Compensation Plan 2019 |  |  |
Share-Based Compensation |  |  |
Restricted stock units outstanding ( in shares) | 32,897 | 25,396 | 27,488
Unrecognized compensation expense | $ 97,954 |  |
Restricted Stock Units | Stock Based Incentive Compensation Plan 2019 | Non-employee directors |  |  |
Share-Based Compensation |  |  |
Share-based compensation expense | 178,000 | $ 160,000 | $ 160,000
Restricted Stock Units | Stock Based Incentive Compensation Plan 2019 | Employee |  |  |
Share-Based Compensation |  |  |
Share-based compensation expense | $ 3,000 | $ 0 | $ 0

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