Long-Term Debt - Additional Information (Details)					3 Months Ended				12 Months Ended
	Nov. 22, 2022 USD ($)	Dec. 17, 2020	Jun. 12, 2020 USD ($)	Jun. 02, 2020 USD ($) Days $ / shares shares	Sep. 30, 2021 USD ($)	Jun. 30, 2021	Mar. 31, 2021	Dec. 31, 2020	Sep. 30, 2022 USD ($)	Sep. 30, 2021 USD ($)	Sep. 30, 2020 USD ($)
Debt Instrument [Line Items]
Proceeds from issuance of notes										$ 0	$ 547,719,000
LIBOR
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate									2.25%
Senior Credit Facilities
Debt Instrument [Line Items]
Pledge equity interests in foreign subsidiaries			65.00%
Minimum liquidity									$ 75,000,000
Debt instrument, covenant description									The Credit Agreement contains certain affirmative and negative covenants customary for financings of this type that, among other things, limit our and our subsidiaries’ ability to incur additional indebtedness or liens, to dispose of assets, to make certain fundamental changes, to designate subsidiaries as unrestricted, to make certain investments, to prepay certain indebtedness and to pay dividends, or to make other distributions or redemptions/repurchases, in respect of our and our subsidiaries’ equity interests. In addition, the Credit Agreement contains financial covenants, each tested quarterly, (1) a net secured leveraged ratio of not greater than 3.25 to 1.00; (2) a net total leverage ratio of not greater than 4.25 to 1.00; and (3) minimum liquidity of at least $75 million. The Credit Agreement also contains events of default customary for financings of this type, including certain customary change of control events. As of September 30, 2022 and 2021, we were in compliance with all Credit Agreement covenants.
Amended Senior Credit Facilities
Debt Instrument [Line Items]
Debt Instrument, interest rate description									The Amendment revised certain interest rates in the Credit Agreement. Following delivery of a compliance certificate for the first full fiscal quarter after the Amendment No. 1 Effective Date, the applicable margins for the revolving credit and term facilities is subject to a pricing grid based upon the net total leverage ratio as follows (i) if the net total leverage ratio is greater than 3.00 to 1.00, the applicable margin is LIBOR plus 3.00% or ABR plus 2.00%; (ii) if the net total leverage ratio is less than or equal to 3.00 to 1.00 but greater than 2.50 to 1.00, the applicable margin is LIBOR plus 2.75% or ABR plus 1.75%; (iii) if the net total leverage ratio is less than or equal to 2.50 to 1.00 but greater than 2.00 to 1.00, the applicable margin is LIBOR plus 2.50% or ABR plus 1.50%; (iv) if the net total leverage ratio is less than or equal to 2.00 to 1.00 but greater than 1.50 to 1.00, the applicable margin is LIBOR plus 2.25% or ABR plus 1.25%; and (v) if the net total leverage ratio is less than or equal to 1.50 to 1.00, the applicable margin is LIBOR plus 2.20% or ABR plus 1.00%. As a result of the Amendment, the applicable LIBOR floor was reduced from 0.50% to 0.00%. From the Amendment No. 1 Effective Date until the fiscal quarter ended December 31, 2020, the interest rate was LIBOR plus 2.50%. For the three months ended March 31, 2021, the interest rate was LIBOR plus 2.25%. For the three months ended June 30, 2021, the interest rate was LIBOR plus 2.25%. For the three months ended September 30, 2021, the interest rate was LIBOR plus 2.25%.
Interest expense									$ 4,300,000	4,100,000	1,500,000
Description of unused line fee									In addition, the quarterly commitment fee required to be paid based on the unused portion of the Revolving Facility is subject to a pricing grid based upon the net total leverage ratio as follows (i) if the net total leverage ratio is greater than 3.00 to 1.00, the unused line fee is 0.500%; (ii) if the net total leverage ratio is less than or equal to 3.00 to 1.00 but greater than 2.50 to 1.00, the unused line fee is 0.450%; (iii) if the net total leverage ratio is less than or equal to 2.50 to 1.00 but greater than 2.00 to 1.00, the unused line fee is 0.400%; (iv) if the net total leverage ratio is less than or equal to 2.00 to 1.00 but greater than 1.50 to 1.00, the unused line fee is 0.350%; and (v) if the net total leverage ratio is less than or equal to 1.50 to 1.00, the unused line fee is 0.300%.
Amended Senior Credit Facilities | LIBOR
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate		0.00%	0.50%		2.25%	2.25%	2.25%	2.50%
Amended 2 Senior Credit Facilities
Debt Instrument [Line Items]
Debt Instrument, interest rate description									Amendment No. 2 revised certain interest rates in the Credit Agreement. The applicable margins for the revolving credit and term facilities is subject to a pricing grid based upon the net total leverage ratio as follows (i) if the net total leverage ratio is greater than 3.00 to 1.00, the applicable margin is SOFR plus 3.00% or ABR plus 2.00%; (ii) if the net total leverage ratio is less than or equal to 3.00 to 1.00 but greater than 2.50 to 1.00, the applicable margin is SOFR plus 2.75% or ABR plus 1.75%; (iii) if the net total leverage ratio is less than or equal to 2.50 to 1.00 but greater than 2.00 to 1.00, the applicable margin is SOFR plus 2.50% or ABR plus 1.50%; (iv) if the net total leverage ratio is less than or equal to 2.00 to 1.00 but greater than 1.50 to 1.00, the applicable margin is SOFR plus 2.25% or ABR plus 1.25%; and (v) if the net total leverage ratio is less than or equal to 1.50 to 1.00, the applicable margin is SOFR plus 2.20% or ABR plus 1.00%. From the Amendment No. 2 Effective Date until delivery of the first compliance certificate after the covenant adjustment period, the applicable margin will be SOFR plus 3.00% or ABR plus 2.00%.
Amended 2 Senior Credit Facilities | Subsequent Event
Debt Instrument [Line Items]
Minimum liquidity	$ 125,000,000
Maximum capital expenditures amount	$ 7,500,000
Amended 2 Senior Credit Facilities | Base Rate | Subsequent Event
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate	2.00%
Amended 2 Senior Credit Facilities | SOFR | Subsequent Event
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate	3.00%
Maximum | Senior Credit Facilities
Debt Instrument [Line Items]
Net leverage ratio									4.25
Net secured leverage ratio									3.25%
Maximum | Amended 2 Senior Credit Facilities | Subsequent Event
Debt Instrument [Line Items]
Net secured leverage ratio	4.25%
3.00% Convertible Senior Notes Due 2025
Debt Instrument [Line Items]
Aggregate principal amount				$ 175,000,000.0
Debt instrument convertible, if-converted value of the Notes less than its principal amount									$ 101,300,000
Debt instrument convertible, if-converted value of the Notes exceeded its principal amount										274,400,000
Debt instrument, interest rate				3.00%					3.00%
Debt Instrument, option to purchase additional principal amount				$ 25,000,000.0
Proceeds from issuance of notes				$ 169,800,000
Debt instrument, maturity date				Jun. 01, 2025
Debt instrument, convertible trading days | Days				20
Debt instrument, convertible consecutive trading days | Days				30
Debt instrument, convertible conversion price percentage				130.00%
Debt instrument, convertible principal amount				$ 1,000
Debt instrument, convertible maximum conversion price percentage				98.00%
Debt instrument, conversion initial rate | shares				26.7271
Debt instrument, convertible principal amount				$ 1,000
Debt instrument, conversion price | $ / shares				$ 37.42
Debt instrument, redemption price percentage of principal amount				100.00%
Debt instrument, sinking fund				$ 0
Debt instrument, percentage of repurchase principal amount				100.00%
Carrying value of debt				$ 155,300,000
Additional paid-in capital in stockholder's equity				19,700,000
Carrying amount of equity component, net of taxes and transaction costs					$ 14,400,000				$ 14,400,000	14,400,000
Transaction costs				5,600,000
Transaction costs amortized as interest expense				5,000,000.0
Transaction costs allocated to equity component recorded as decrease in additional paid-in capital				$ 600,000
Interest expense									$ 9,945,000	9,660,000	$ 3,169,000
3.00% Convertible Senior Notes Due 2025 | Minimum
Debt Instrument [Line Items]
Debt instrument, convertible trading days | Days				20
Debt instrument, convertible conversion price percentage				130.00%
3.00% Convertible Senior Notes Due 2025 | Maximum
Debt Instrument [Line Items]
Debt instrument covenants, percentage of aggregate principal amount payable.				25.00%
Four Year Senior Secured Term Loan Facility | Senior Credit Facilities
Debt Instrument [Line Items]
Debt instrument term			4 years
Credit facility maximum borrowing capacity			$ 125,000,000.0
Net proceeds from issuance of credit facility			123,000,000.0
Four Year Senior Secured Term Loan Facility | Amended Senior Credit Facilities
Debt Instrument [Line Items]
Debt instrument periodic payments equivalent percentage of annual amount on original principal amount during first two years		1.25%
Debt instrument, frequency of periodic principal payments									quarterly
Debt instrument periodic payments equivalent percentage of annual amount on original principal amount after two years		2.50%
Senior Secured First-lien Revolving Credit Facility | Senior Credit Facilities
Debt Instrument [Line Items]
Credit facility maximum borrowing capacity			$ 50,000,000.0
Outstanding amount under credit facility					$ 0				$ 0	$ 0
Net Leverage Ratio Greater Than 3.00 | Amended Senior Credit Facilities
Debt Instrument [Line Items]
Net leverage ratio		3.00
Unused line fee percentage		50.00%
Net Leverage Ratio Greater Than 3.00 | Amended Senior Credit Facilities | LIBOR
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate		3.00%
Net Leverage Ratio Greater Than 3.00 | Amended Senior Credit Facilities | Base Rate
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate		2.00%
Net Leverage Ratio Greater Than 3.00 | Amended 2 Senior Credit Facilities | Subsequent Event
Debt Instrument [Line Items]
Net leverage ratio	3.00
Net Leverage Ratio Greater Than 3.00 | Amended 2 Senior Credit Facilities | Base Rate | Subsequent Event
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate	2.00%
Net Leverage Ratio Greater Than 3.00 | Amended 2 Senior Credit Facilities | SOFR | Subsequent Event
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate	3.00%
Net Leverage Ratio Less Than or Equal to 3.00 but Greater Than 2.50 | Amended Senior Credit Facilities
Debt Instrument [Line Items]
Unused line fee percentage		45.00%
Net Leverage Ratio Less Than or Equal to 3.00 but Greater Than 2.50 | Amended Senior Credit Facilities | LIBOR
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate		2.75%
Net Leverage Ratio Less Than or Equal to 3.00 but Greater Than 2.50 | Amended Senior Credit Facilities | Base Rate
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate		1.75%
Net Leverage Ratio Less Than or Equal to 3.00 but Greater Than 2.50 | Amended 2 Senior Credit Facilities | Base Rate | Subsequent Event
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate	1.75%
Net Leverage Ratio Less Than or Equal to 3.00 but Greater Than 2.50 | Amended 2 Senior Credit Facilities | SOFR | Subsequent Event
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate	2.75%
Net Leverage Ratio Less Than or Equal to 3.00 but Greater Than 2.50 | Minimum | Amended Senior Credit Facilities
Debt Instrument [Line Items]
Net leverage ratio		2.50
Net Leverage Ratio Less Than or Equal to 3.00 but Greater Than 2.50 | Minimum | Amended 2 Senior Credit Facilities | Subsequent Event
Debt Instrument [Line Items]
Net leverage ratio	2.50
Net Leverage Ratio Less Than or Equal to 3.00 but Greater Than 2.50 | Maximum | Amended Senior Credit Facilities
Debt Instrument [Line Items]
Net leverage ratio		3.00
Net Leverage Ratio Less Than or Equal to 3.00 but Greater Than 2.50 | Maximum | Amended 2 Senior Credit Facilities | Subsequent Event
Debt Instrument [Line Items]
Net leverage ratio	3.00
Net Leverage Ratio Less Than or Equal to 2.50 but Greater Than 2.00 | Amended Senior Credit Facilities
Debt Instrument [Line Items]
Unused line fee percentage		40.00%
Net Leverage Ratio Less Than or Equal to 2.50 but Greater Than 2.00 | Amended Senior Credit Facilities | LIBOR
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate		2.50%
Net Leverage Ratio Less Than or Equal to 2.50 but Greater Than 2.00 | Amended Senior Credit Facilities | Base Rate
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate		1.50%
Net Leverage Ratio Less Than or Equal to 2.50 but Greater Than 2.00 | Amended 2 Senior Credit Facilities | Base Rate | Subsequent Event
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate	1.50%
Net Leverage Ratio Less Than or Equal to 2.50 but Greater Than 2.00 | Amended 2 Senior Credit Facilities | SOFR | Subsequent Event
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate	2.50%
Net Leverage Ratio Less Than or Equal to 2.50 but Greater Than 2.00 | Minimum | Amended Senior Credit Facilities
Debt Instrument [Line Items]
Net leverage ratio		2.00
Net Leverage Ratio Less Than or Equal to 2.50 but Greater Than 2.00 | Minimum | Amended 2 Senior Credit Facilities | Subsequent Event
Debt Instrument [Line Items]
Net leverage ratio	2.00
Net Leverage Ratio Less Than or Equal to 2.50 but Greater Than 2.00 | Maximum | Amended Senior Credit Facilities
Debt Instrument [Line Items]
Net leverage ratio		2.50
Net Leverage Ratio Less Than or Equal to 2.50 but Greater Than 2.00 | Maximum | Amended 2 Senior Credit Facilities | Subsequent Event
Debt Instrument [Line Items]
Net leverage ratio	2.50
Net Leverage Ratio Less Than or Equal to 2.00 but Greater Than 1.50 | Amended Senior Credit Facilities
Debt Instrument [Line Items]
Unused line fee percentage		35.00%
Net Leverage Ratio Less Than or Equal to 2.00 but Greater Than 1.50 | Amended Senior Credit Facilities | LIBOR
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate		2.25%
Net Leverage Ratio Less Than or Equal to 2.00 but Greater Than 1.50 | Amended Senior Credit Facilities | Base Rate
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate		1.25%
Net Leverage Ratio Less Than or Equal to 2.00 but Greater Than 1.50 | Amended 2 Senior Credit Facilities | Base Rate | Subsequent Event
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate	1.25%
Net Leverage Ratio Less Than or Equal to 2.00 but Greater Than 1.50 | Amended 2 Senior Credit Facilities | SOFR | Subsequent Event
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate	2.25%
Net Leverage Ratio Less Than or Equal to 2.00 but Greater Than 1.50 | Minimum | Amended Senior Credit Facilities
Debt Instrument [Line Items]
Net leverage ratio		1.50
Net Leverage Ratio Less Than or Equal to 2.00 but Greater Than 1.50 | Minimum | Amended 2 Senior Credit Facilities | Subsequent Event
Debt Instrument [Line Items]
Net leverage ratio	1.50
Net Leverage Ratio Less Than or Equal to 2.00 but Greater Than 1.50 | Maximum | Amended Senior Credit Facilities
Debt Instrument [Line Items]
Net leverage ratio		2.00
Net Leverage Ratio Less Than or Equal to 2.00 but Greater Than 1.50 | Maximum | Amended 2 Senior Credit Facilities | Subsequent Event
Debt Instrument [Line Items]
Net leverage ratio	2.00
Net Leverage Ratio Less Than or Equal to 1.50 | Amended Senior Credit Facilities
Debt Instrument [Line Items]
Net leverage ratio		1.50
Unused line fee percentage		30.00%
Net Leverage Ratio Less Than or Equal to 1.50 | Amended Senior Credit Facilities | LIBOR
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate		2.20%
Net Leverage Ratio Less Than or Equal to 1.50 | Amended Senior Credit Facilities | Base Rate
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate		1.00%
Net Leverage Ratio Less Than or Equal to 1.50 | Amended 2 Senior Credit Facilities | Subsequent Event
Debt Instrument [Line Items]
Net leverage ratio	1.50
Net Leverage Ratio Less Than or Equal to 1.50 | Amended 2 Senior Credit Facilities | Base Rate | Subsequent Event
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate	1.00%
Net Leverage Ratio Less Than or Equal to 1.50 | Amended 2 Senior Credit Facilities | SOFR | Subsequent Event
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate	2.20%