Long-Term Debt - Additional Information (Details)						3 Months Ended	12 Months Ended
	Jun. 26, 2023 USD ($) Days $ / shares shares	Nov. 22, 2022 USD ($)	Dec. 17, 2020	Jun. 12, 2020 USD ($)	Jun. 02, 2020 USD ($) Days $ / shares shares	Dec. 31, 2023 USD ($)	Sep. 30, 2023 USD ($)	Sep. 30, 2022 USD ($)	Sep. 30, 2021 USD ($)	Jul. 03, 2023 USD ($)	Mar. 31, 2023 USD ($)
Debt Instrument [Line Items]
Aggregate principal amount							$ 297,500,000	$ 285,938,000
Loss on extinguishment of debt							(1,333,000)
Payment on debt issuance costs							17,176,000		$ 520,000
Proceeds from issuance of notes							210,000,000
Long-Term Debt							275,951,000	270,374,000
Debt unamortized issuance costs, net							17,753,000	2,990,000
Debt, principal amount, net							$ 297,500,000
Senior Credit Facilities
Debt Instrument [Line Items]
Aggregate principal amount								$ 110,938,000
Debt instrument, maturity date								Apr. 01, 2025
Long-Term Debt								$ 109,470,000
Debt unamortized issuance costs, net								158,000
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 leverage 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.
Amended Senior Credit Facilities
Debt Instrument [Line Items]
Debt Instrument, interest rate description							Amendment No. 1 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 Amendment No 1, the applicable LIBOR floor was reduced from 0.50% to 0.00%.
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 | L I B O R
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate			0.00%	0.50%
Credit Agreement Amendment Two
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 10 basis point credit spread adjustment 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 10 basis point credit spread adjustment 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 10 basis point credit spread adjustment 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 10 basis point credit spread adjustment 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 10 basis point credit spread adjustment plus 2.20% or ABR plus 1.00%. During the covenant adjustment period, and until the delivery of a compliance certificate for the first full fiscal quarter after the covenant adjustment period, the applicable margin will be SOFR plus 10 basis point credit spread adjustment plus 3.00% or ABR plus 2.00%. In connection with the issuance of the 2028 Notes, we borrowed $24.7 million under our Revolving Facility and paid $106.3 million towards our Term Loan Facility. As a result, we recorded $104.9 million extinguishment of debt and $1.3 million loss on the extinguishment of debt. All principal and interest on the Term Loan Facility have been paid in full. On July 3, 2023, we repaid the outstanding balance on our Revolving Facility. As of September 30, 2023 and 2022, there were no amounts outstanding under the Revolving Facility. Total interest expense relating to the Senior Credit Facilities for the fiscal year ended September 30, 2023, 2022 and 2021 was $6.7 million, $4.3 million, $4.1 million, respectively, reflecting the coupon and accretion of the discount.
Interest expense							$ 6,700,000	4,300,000	$ 4,100,000
Minimum liquidity											$ 125,000,000
Payment of refinancing fees to lender		$ 400,000
Payment of refinancing fees to third party		$ 100,000
Credit Agreement Amendment Two | Forecast
Debt Instrument [Line Items]
Maximum capital expenditures amount						$ 7,500,000
Credit Agreement Amendment Two | Base Rate
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate		2.00%
Credit Agreement Amendment Two | SOFR
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate		0.10%
Credit Agreement Amendment Two | SOFR plus Ten Basis Point Credit Spread Member
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate		3.00%
Maximum
Debt Instrument [Line Items]
Percentage of the remaining cash flow of original instrument							10.00%
Maximum | Senior Credit Facilities
Debt Instrument [Line Items]
Net leverage ratio							4.25
Net secured leverage ratio							3.25%
Maximum | Credit Agreement Amendment Two | Forecast
Debt Instrument [Line Items]
Net secured leverage ratio						4.25%
1.50% Convertible Senior Notes Due 2028
Debt Instrument [Line Items]
Aggregate principal amount	$ 190,000,000						$ 122,500,000
Payment on debt issuance costs							2,400,000
Debt instrument convertible, if-converted value of the Notes less than its principal amount							$ 61,200,000
Debt instrument, interest rate	1.50%						1.50%
Debt Instrument, option to purchase additional principal amount										$ 20,000,000
Proceeds from issuance of notes	$ 193,200,000
Debt instrument, maturity date	Jul. 01, 2028						Jul. 01, 2028
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	24.5586
Debt instrument, convertible principal amount	$ 1,000
Debt instrument, conversion price | $ / shares	$ 40.72
Debt instrument, redemption price percentage of principal amount	100.00%
Debt instrument, sinking fund	$ 0
Debt instrument, percentage of repurchase principal amount	100.00%
Long-Term Debt							$ 120,229,000
Debt unamortized issuance costs, net							2,271,000
Debt, principal amount, net							122,500,000
Unamortized issuance costs							2,300,000
1.50% Convertible Senior Notes Due 2028 | Additional Paid-in-Capital
Debt Instrument [Line Items]
Fair value of the embedded conversion feature							4,100,000
1.50% Convertible Senior Notes Due 2028 | Minimum
Debt Instrument [Line Items]
Debt instrument, convertible trading days | Days	20
Debt instrument, convertible conversion price percentage	130.00%
1.50% Convertible Senior Notes Due 2028 | Maximum
Debt Instrument [Line Items]
Debt instrument covenants, percentage of aggregate principal amount payable.	25.00%
3.00% Convertible Senior Notes Due 2025
Debt Instrument [Line Items]
Aggregate principal amount					$ 175,000,000		87,500,000	175,000,000
Debt instrument convertible, if-converted value of the Notes less than its principal amount							$ 83,600,000	$ 101,300,000
Debt instrument, interest rate					3.00%		3.00%	3.00%
Debt Instrument, option to purchase additional principal amount					$ 25,000,000
Proceeds from issuance of notes					$ 169,800,000
Debt instrument, maturity date					Jun. 01, 2025		Jun. 01, 2025	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%
Debt instrument repurchase amount							$ 87,500,000
Long-Term Debt							86,508,000	$ 160,904,000
Debt unamortized issuance costs, net							992,000	2,832,000
Debt, principal amount, net							$ 175,000,000
Carrying amount of equity component, net of taxes and transaction costs								14,400,000
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%
Conversion feature percentage							10.00%
3.00% Convertible Senior Notes Due 2025 | Maximum
Debt Instrument [Line Items]
Debt instrument covenants, percentage of aggregate principal amount payable.					25.00%
1.50% Convertible Senior Notes Due 2025
Debt Instrument [Line Items]
Aggregate principal amount							$ 87,500,000
Payment on debt issuance costs							$ 14,300,000
Debt instrument, interest rate							1.50%
Debt instrument, maturity date							Jul. 01, 2028
Long-Term Debt							$ 69,214,000
Debt unamortized issuance costs, net							14,490,000
Payment of refinancing fees to lender							3,800,000
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 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]
Aggregate principal amount							24,700,000
Debt repayment cost							106,300,000
Extinguishment of debt							104,900,000
Loss on extinguishment of debt							1,300,000
Revolving credit facility outstanding amount							0	$ 0
Credit facility maximum borrowing capacity				$ 50,000,000.0
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 | L I B O R
Debt Instrument [Line Items]
Net leverage ratio			3.00
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 | Credit Agreement Amendment Two
Debt Instrument [Line Items]
Net leverage ratio		3
Net Leverage Ratio Greater Than 3.00 | Credit Agreement Amendment Two | Base Rate
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate		2.00%
Net Leverage Ratio Greater Than 3.00 | Credit Agreement Amendment Two | SOFR
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate		0.10%
Net Leverage Ratio Greater Than 3.00 | Credit Agreement Amendment Two | SOFR plus Ten Basis Point Credit Spread Member
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 | L I B O R
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 | Credit Agreement Amendment Two | 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 | Credit Agreement Amendment Two | SOFR
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate		0.10%
Net Leverage Ratio Less Than or Equal to 3.00 but Greater Than 2.50 | Credit Agreement Amendment Two | SOFR plus Ten Basis Point Credit Spread Member
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 | Credit Agreement Amendment Two
Debt Instrument [Line Items]
Net leverage ratio		2.5
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 | Credit Agreement Amendment Two
Debt Instrument [Line Items]
Net leverage ratio		3
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 | L I B O R
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 | Credit Agreement Amendment Two | 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 | Credit Agreement Amendment Two | SOFR
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate		0.10%
Net Leverage Ratio Less Than or Equal to 2.50 but Greater Than 2.00 | Credit Agreement Amendment Two | SOFR plus Ten Basis Point Credit Spread Member
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 | Credit Agreement Amendment Two
Debt Instrument [Line Items]
Net leverage ratio		2
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 | Credit Agreement Amendment Two
Debt Instrument [Line Items]
Net leverage ratio		2.5
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 | L I B O R
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 | Credit Agreement Amendment Two | 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 | Credit Agreement Amendment Two | SOFR
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate		0.10%
Net Leverage Ratio Less Than or Equal to 2.00 but Greater Than 1.50 | Credit Agreement Amendment Two | SOFR plus Ten Basis Point Credit Spread Member
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 | Credit Agreement Amendment Two
Debt Instrument [Line Items]
Net leverage ratio		1.5
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 | Credit Agreement Amendment Two
Debt Instrument [Line Items]
Net leverage ratio		2
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 | L I B O R
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 | Credit Agreement Amendment Two
Debt Instrument [Line Items]
Net leverage ratio		1.5
Net Leverage Ratio Less Than or Equal to 1.50 | Credit Agreement Amendment Two | 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 | Credit Agreement Amendment Two | SOFR
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate		0.10%
Net Leverage Ratio Less Than or Equal to 1.50 | Credit Agreement Amendment Two | SOFR plus Ten Basis Point Credit Spread Member
Debt Instrument [Line Items]
Debt Instrument, basis spread on variable rate		2.20%
Modified Notes
Debt Instrument [Line Items]
Long-Term Debt							155,700,000
Debt unamortized issuance costs, net							$ 19,300,000